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Professor  Raymond’s  System  of  COMPARATIVE  /ESTHETICS 

I.  — Art  in  Theory.  8°,  cloth  extra  ......  $t.75 

“ Scores  an  advance  upon  the  many  art-criticisms  extant.  . . . Twenty  brilliant  chap- 
ters, pregnant  with  suggestion.” — Popular  Science  Monthly. 

“A  well  grounded,  thoroughly  supported,  and  entirely  artistic  conception  of  art  that  will 
lead  observers  to  distrust  the  charlatanism  that  imposes  an  idle  and  superficial  mannerism 
upon  the  public  in  place  of  true  beauty  and  honest  workmanship.” — The  New  York 
Times. 

“His  style  is  good,  and  his  logic  sound,  and  ...  of  the  greatest  possible  service  to  the 
student  of  artistic  theories.” — Art  Jojtrnal  (London). 

II.  — The  Representative  Significance  of  Form.  8°,  cloth  extra.  $2.00 

“A  valuable  essay.  . , . Professor  Raymond  goes  so  deep  into  causes  as  to  explore  the 
subconscious  and  the  unconscious  mind  for  a solution  of  his  problems,  and  eloquently  to 
range  through  the  conceptions  of  religion,  science  and  metaphysics  in  order  to  find  fixed 
principles  of  taste.  . . . A highly  interesting  discussion.’’ — The  Scotsman  (Edinburgh). 

“ Evidently  the  ripe  fruit  of  years  of  patient  and  exhaustive  study  on  the  part  of  a man 
singularly  fitted  for  his  task.  1 1 is  profound  in  insight,  searching  in  analysis,  broad  in 
spirit,  and  thoroughly  modern  in  method  and  sympathy.” — The  Universalist  Leader. 

“Its  title  gives  no  intimation  to  the  general  reader  of  its  attractiveness  for  him,  or  to 
curious  readers  of  its  widely  discursive  range  of  interest.  ...  Its  broad  range  may  re- 
mind one  of  those  scythe-bearing  chariots  with  which  the  ancient  Persians  used  to  mow 
down  hostile  files.” — The  Outlook. 

III.  — Poetry  as  a Representative  Art.  8°,  cloth  extra  . $1.75 

44 1 have  read  it  with  pleasure,  and  a sense  of  instruction  on  many  points.” — Francis 
Turner  Palgravey  Professor  of  Poetry , Oxford  University. 

44  Dieses  ganz  vortreffliche  Werk.” — Englische  Studien , Universitat  Breslau. 

“An  acute,  interesting,  and  brilliant  piece  of  work.  . . . As  a.  whole  the  essay  deserves 
unqualified  praise.” — IV.  Y.  Independe7it. 

IV.  — Painting,  Sculpture,  and  Architecture  as  Representative  Arts. 

With  225  illustrations.  8°  .....  $2.50 

# 44  The  artist  will  find  in  it  a wealth  of  profound  and  varied  learning ; of  original,  sugges- 
tive, helpful  thought  . . . of  absolutely  inestimable  value.” — The  Looker-on. 

‘‘Expression  by  means  of  extension  or  size,  . . . shape,  . . . regularity  in  outlines 
...  the  human  body  . . . posture,  gesture,  and  movement,  . . . are  all  considered 
...  A specially  interesting  chapter  is  the  one  on  color.” — Current  Literature . 

4‘  The  whole  book  is  the  work  of  a man  of  exceptional  thoughtfulness,  who  says  what 
he  has  to  say  in  a remarkably  lucid  and  direct  manner.” — Philadelphia  Press. 

V.  — The  Genesis  of  Art  Form.  Fully  illustrated.  8°  . . $2.25 

44  In  a spirit  at  once  scientific  and  that  of  the  true  artist,  he  pierces  through  the  mani- 
festations of  art  to  their  sources,  and  shows  the  relations,  intimate  and  essential,  between 
painting,  sculpture,  poetry,  music,  and  architecture.  A book  that  possesses  not  only  sin- 
gular value,  but  singular  charm.” — IV.  V.  Times. 

44 A help  and  a delight.  Every  aspirant  for  culture  in  any  of  the  liberal  arts,  including 
music  and  poetry,  will  find  something  in  this  book  to  aid  him.” — Boston  Times.  * 

44  It  is  impossible  to  withhold  one’s  admiration  from  a treatise  which  exhibits  in  such  a 
large  degree  the  qualities  of  philosophic  criticism.” — Philadelphia  Press. 

VI.  — Rhythm  and  Harmony  in  Poetry  and  Music.  Together  with 

Music  as  a Representative  Art.  8°,  cloth  extra  . $1.75 

44  Prof.  Raymond  has  chosen  a delightful  subject,  and  he  treats  it  with  all  the  charm  of 
narrative  and  high  thought  and  profound  study.” — Ne7u  Orleans  States. 

“The  reader  must  be,  indeed,  a person  either  of  supernatural  stupidity  or  of  marvellous 
erudition,  who  does  not  discover  much  information  in  Prof.  Raymond's  exhaustive  and 
instructive  treatise.  From  page  to  page  it  is  full  of  suggestion.” — The  Academy  (London). 

VII.  — Proportion  and  Harmony  of  Line  and  Color  in  Painting, 

Sculpture,  and  Architecture.  Fully  illustrated.  8°  . $2.50 

44  Marked  by  profound  thought  along  lines  unfamiliar  to  most  readers  and  thinkers.  . . 

When  grasped,  however,  it  becomes  a source  of  great  enjoyment  and  exhilaration.  . . . No 
critical  person  can  afford  to  ignore  so  valuable  a contribution  to  the  art-thought  of  the 
day.” — The  Art  Interchange  (N.  Y ).  # 

44  One  does  not  need  to  be  a scholar  to  follow  this  scholar  as  he  teaches  while  seeming  to 
entertain,  for  he  does  both.” — Burlington  Havokeye. 

44  The  artist  who  wishes  to  penetrate  the  mysteries  of  color,  the  sculptor  who  desires  to 
cultivate  his  sense  of  proportion,  or  the  architect  whose  ambition  is  to  reach  to  a high 
•tandard  will  find  the  work  helpful  and  inspiring.” — Boston  Transcript. 

G.  P.  PUTNAM’S  SONS,  New  York  and  London 


iVff 


PROPORTION  AND 


n 


HARMONY 


OF 


LINE  AND  COLOR 


IN 


PAINTING,  SCULPTURE,  AND  ARCHITECTURE 


PROFESSOR  OF  ESTHETICS  IN  PRINCETON  UNIVERSITY;  AUTHOR  OF  “ART  IN  THEORY,’* 
“THE  REPRESENTATIVE  SIGNIFICANCE  OF  FORM,”  “POETRY  AS  A REPRESENT- 
ATIVE ART,”  “ PAINTING,  SCULPTURE,  AND  ARCHITECTURE  AS  REPRESENT- 
ATIVE ARTS,”  “THE  GENESIS  OF  ART-FORM,”  “ RHYTHM  AND 
HARMONY  IN  POETRY  AND  MUSIC,”  “THE  ESSENTIALS 
OF  ./ESTHETICS,”  ETC. 


AN  ESSAY  IN 


COMPARATIVE  AESTHETICS 


BY 


GEORGE  LANSING  RAYMOND,  L.H.D. 


SECOND  EDITION  REVISED 


G.  P.  PUTNAM’S  SONS 


NEW  YORK 


LONDON 

24  BEDFORD  STREET  STRAND 


27  WEST  TWENTY-THIRD  STREET 


finuktibochtr  J)«bs 


Copyright,  1899 

BY 

G.  P.  PUTNAM’S  SONS 
Entered  at  Stationers’  Hall,  London 


Ube  Utnlcfceibocber  iprees,  IRew  JfforB 


n oi.i7 

■tfSL^C 

PREFACE.  / . 


T N many  important  regards  the  conceptions  and  conclu- 
sions of  this  volume  differ  from  those  ordinarily  pre- 
sented with  reference  to  the  subjects  of  which  it  treats. 
When  considering,  for  instance,  the  first  of  the  two 
general  topics  discussed,  the  view  expressed  in  Gwilt’s 
‘ Encyclopedia  of  Architecture,”  and  still  quite  preva- 
lent, to  the  effect  that  proportion  is  “ but  a synonym  for 
fitness,”  is  entirely  ignored.  This  is  not  because  of  any 
undervaluation  of  the  aesthetic  importance  of  fitness,  but 
because  it  is  recognized  that  this  latter  characterizes  many 
other  artistic  arrangements  of  form,  as  those  of  rhythm, 
tune,  and  color;  and  because  it  is  recognized  also  that 
no  amount  of  mere  fitness  could  cause,  or  even  suggest, 
that  which  is  generally  meant  not  only  by  artists  but  by 
people  in  general  when  they  speak  of  proportion.  When 
using  this  term  in  any  strict  or  technical  sense  they  almost 
invariably  refer  to  an  effect  of  measurements  indicating  a 
certain  mathematical  relationship  between  the  parts  of  a 
product  as  compared  with  one  another  and  with  the  whole. 

This  effect  of  proportion  thus  interpreted  is  further 
limited  in  this  book  by  being  ascribed  to  measurements 
that  are  apparent  as  distinguished  from  actual.  It  is 
shown  that  we  judge  of  the  proportions  of  the  parts  of  a 
body  or  of  a building  when  viewing  each  from  a distance, 
not  when  examining  it  near  at  hand.  This  conclusion  is 
reached  and  emphasized  by  pointing  out  the  difference 
between  proportion  and  perspective.  It  is  shown  that 


IV 


PREFACE. 


perspective,  to  which  several  chapters  are  devoted,  has  to 
do  with  the  methods  of  arranging  real  outlines  and  with 
them,  of  course,  measurements,  so  as  to  have  them  pro- 
duce a certain  desired  visual  result,  whereas  proportion 
has  to  do  with  the  measurements  as  they  appear  in  the 
result  after  perspective  has  produced  it. 

Again  the  effect  of  proportion  is  attributed  in  this 
volume  to  the  mind’s  conscious  as  distinguished  from  un- 
conscious measurements.  This  distinction  is  the  logical 
result  of  a conception  of  an  essential  correspondence  be- 
tween proportion  and  rhythm.  In  the  latter  the  mind  is 
always  consciously  able  to  count,  if  it  choose,  the  notes, 
syllables,  feet,  bars,  lines,  phrases — in  other  words  the 
measures  or  measurements — which  cause  the  effect.  This 
is  the  same  as  to  say  that  proportion  in  the  arts  of  sight 
is  not,  as  has  been  almost  universally  supposed  (see  Chap- 
ter III.),  the  analogue  of  harmony  in  the  arts  of  sound. 
Harmony  is  produced  in  these  arts  whenever  the  number 
of  vibrations  per  second  determining  the  pitch  of  one  tone 
sustains  a certain  ratio  to  the  number  of  vibrations  per 
second  determining  the  pitch  of  another  tone.  But  only 
the  investigations  of  science  have  been  able  to  discover 
that  this  is  the  reason  for  the  effect.  The  mind  cannot 
count  the  vibrations.  It  is  not  conscious  of  them;  but 
only  of  an  agreeable  thrill  or  glow  in  case  they  coalesce, 
as  they  do  when  they  sustain  to  one  another  the  required 
harmonic  ratio.  Now  if  we  go  upon  the  supposition  that 
the  measurements  determining  the  effects  of  proportion 
are  perceived  just  as  are  those  determining  the  effects 
of  harmony,  it  is  evident  that  we  must  suppose  ourselves 
dealing  with  factors  of  which  the  mind  is  unconscious; 
and  must  remain  ignorant  until  science  has  come  into 
possession  of  certain  data  not  yet  discovered.  Is  it  any 


PREFA  CE. 


V 


wonder  that  those  accepting  this  supposition  who  have 
tried  to  explain  the  effects,  have  either  held  that  they 
cannot  be  explained  at  all,  or  have  made  attempts  at  ex- 
planation which  may  be  said  in  a general  way  to  have 
failed  to  prove  convincing  ? Is  it  any  wonder  that,  even 
when  acknowledging  that  the  Greeks  once  had  a know- 
ledge of  the  subject,  very  many  in  our  own  times,  after 
seeking  for  this  knowledge  in  wrong  directions,  have  con- 
ceived of  the  subject  as  hidden  in  almost  impenetrable 
mystery, — as  involving  principles  which  it  is  wellnigh 
useless  for  present  artists  to  attempt  either  to  understand 
or  to  apply  ? 

Once  more,  artistic  proportion  is  based  in  this  volume, 
as  all  acknowledge  rhythm  to  be,  upon  the  principle  of 
comparison.  It  is  held  that,  fundamentally,  measure- 
ments go  together  because  they  appear  to  be  exactly 
alike,  that  is,  as  I : I ; and  that  the  mind  accepts  the 
ratios  of  certain  small  numbers  that  are  not  alike,  like 
i :2  or  2:3,  because  it  is  able  to  recognize  in  the  first 
that  which  corresponds  to  1 : 1 — |—  1,  and  in  the  second 
that  which  corresponds  to  I -f-  1 : I — f-  1 — {—  1 . Finally, 
connected  with  this,  it  is  shown  that  as  rhythm  starts  by 
putting  together  similar  small  parts  such  as  feet  and  lines, 
and  produces  the  general  effect  of  the  whole  as  a result 
of  the  combined  effects  of  these  parts,  so  does  artistic 
proportion.  For  instance,  the  height  of  the  front  of  the 
Parthenon  is  to  its  breadth  as  4:9.  But  we  need  not 
consider  the  architect  as  aiming  primarily  at  this  propor- 
tion ; or  that  it  is  any  more  than  a secondary,  though,  of 
course,  a necessary  result  of  the  relations,  the  one  to  the 
other,  of  the  different  separate  measurements  put  together 
in  order  to  form  the  whole. 

The  distinctions  thus  made  seem  important  theoreti- 


VI 


PREFACE. 


cally,  not  merely  because  of  their  rendering  logically 
consistent,  according  to  the  principles  of  comparative 
aesthetics,  the  correspondences  indicated  between  propor- 
tion and  rhythm  on  the  one  hand,  and  between  color  and 
tone  on  the  other;  but  also  because  of  their  rendering 
comprehensible  the  particular  art-effects  to  which  they 
are  applied.  But  the  distinctions  seem  equally  important 
practically.  Only  as  the  effects  of  proportion  are  sepa- 
rated from  those  of  perspective,  and  the  limitations  of 
each  are  perceived  and  determined,  can  the  methods 
underlying  each  be  successfully  applied  to  products. 
There  may  be  a simplicity  of  result  in  the  conclusions 
reached,  reminding  the  reader  of  the  story  of  the  egg 
which  Columbus,  by  smashing  on  a table,  made  to  “ stand 
on  its  end.”  But  simplicity  is  the  door  through  which 
alone  intelligence  can  enter  into  the  complex.  As  in- 
dicated in  either  opinion  or  production,  the  artistic 
intelligence  of  our  own  time  has,  as  yet,  scarcely  an 
apprehension,  and  no  comprehension  whatever,  of  that 
which  is  acknowledged  to  have  formed  the  chief  visual 
excellence  of  Greek  art.  The  author  is  convinced  that 
this  fact  is  owing  almost  wholly  to  a misunderstanding 
of  the  aims  of  proportion,  together  with  a confounding 
of  it  with  perspective. 

Besides  treating  of  these  two  subjects,  this  volume 
contains,  as  applied  to  measurement,  or  size,  as  well  as 
to  what  is  termed  harmony  of  outline,  or  shape,  several 
deductions  not  noticed  in  other  works,  which  it  is  thought 
will  in  a new  way  emphasize  the  importance  as  well  as  in- 
terpret the  meaning,  as  used  in  the  wholes  or  parts  of 
contours,  of  the  curved  line,  and  especially,  as  suggested 
by  the  phenomena  of  binocular  vision,  of  that  of  the 
circle,  the  ellipse,  and  the  parabola. 


PREFA  CE. 


vii 

In  dealing  with  that  much-disputed  subject,  the  har- 
mony of  color,  the  author  has  been  careful  to  incorporate 
enough  that  has  been  said  by  others  to  give  the  reader  a 
general  conception  of  such  opinions  as  may  be  considered 
the  most  trustworthy  and  authoritative.  As  influencing 
practice,  his  own  conclusions  will  be  found  to  coincide 
with  these.  As  influencing  theory,  his  method  of  reach- 
ing his  conclusions  will  be  found  in  several  regards  to  be 
different.  For  this  fact,  no  apology  need  be  offered. 
The  musical  notes  harmonized  by  Pythagoras  do  not  differ 
essentially  from  those  harmonized  by  Helmholtz.  But 
no  one  who  thinks,  questions  the  philosophic  value  of  the 
very  different  reason  for  thus  using  the  notes  which  is 
given  by  the  latter.  In  the  volume  of  this  series  entitled 
“ Rhythm  and  Harmony  in  Poetry  and  Music,”  each  of 
the  art-methods  mentioned  in  the  chart  on  page  3 was 
shown  to  exert  an  influence  in  securing  the  general  effect 
of  harmony  of  tone;  and  in  this  book  the  same  methods 
are  shown  to  exert  a corresponding  influence  in  securing 
harmony  of  color.  But,  in  connection  with  this  fact,  it 
seemed  aesthetically  desirable  to  show  that,  in  particular, 
the  physiological  effect  which  is  most  essential  to  harmony 
— the  effect  which,  in  these  volumes,  has  been  termed 
consonance— is  in  both  sound  and  color  similarly  condi- 
tioned. In  sound,  we  know  it  to  be  a result  of  vibrations 
produced  in  the  ear  by  external  sound-waves  which  are 
related  to  one  another  according  to  certain  ratios.  In 
color  why  should  it  not  be  a result  of  external  light-waves 
similarly  related  ? More  weight  is  attached  in  this  book 
to  this  supposition  than  some  may  deem  warranted. 
Perhaps  the  most  important  objection  to  the  theory  is 
the  phenomenon  of  the  two  complementary  colors  which 
are  invariably  produced,  at  least  potentially,  wherever 


Vlll 


PREFACE. 


one  color  is  produced.  To  this  phenomenon,  at  first 
thought,  there  seems  to  be  no  actual  correspondence 
among  the  sounds.  But  certain  facts  are  adduced  to 
show  that  there  is  more  of  a correspondence  than  at  first 
appears;  and  that,  even  though  it  were  lacking,  this  cir- 
cumstance would  not  necessarily  lessen  the  possibility  of 
a correspondence  between  the  methods  of  operation  of 
the  waves  of  sound  and  of  light.  The  complementary 
colors  may  be  attributed  solely  to  the  eye’s  organism. 
This  may  be  supposed  to  be  so  constituted  that,  when  a 
wave  of  light  is  divided  into  two  parts,  as  it  always  is 
potentially  when  a given  color  is  produced,  each  par- 
ticular organ  of  perception  influenced  by  light  is  also 
divided  into  two  parts,  and  in  such  a way  that  the  mind 
is  directly  conscious  of  only  the  effect  produced  in  that 
part  which  is  nearest  the  optic  nerve-fibre.  In  the  eye, 
each  of  the  organs  which  we  know  to  be  particularly  in- 
strumental in  recognizing  color  is  found  to  have  an  outer 
separated  from  an  inner  limb,  the  one  nearer  the  optic 
nerve-fibre  than  the  other.  Moreover,  of  these  organs 
themselves,  there  are  two  different  kinds — rods  and 
cones.  Whether  we  consider  the  two  limbs,  or  the  two 
organs  containing  them,  therefore,  the  conditions  just 
indicated  as  presumably  necessary  to  the  effects  of  com- 
plementary color  are  present.  In  the  text,  certain  reasons 
are  given  why  the  rods  may  be  supposed  to  be  affected 
mainly  by  light  in  general,  or  atmosphere,  and  the  cones 
by  what  is  termed  local  color.  But  whether  this  be  the 
case  or  not,  both,  of  course,  according  to  the  supposition 
just  advanced,  must  manifest  complementary  hues;  and 
both,  as  will  be  noticed,  have  two  limbs,  and  therefore 
can  realize  the  condition  indicated  as  necessary  for  the 
two  results. 


PREFACE. 


IX 


However,  when  treating  of  a problem  which  so  many 
far  abler  investigators  have  failed  to  solve  satisfactorily, 
it  will  not  do  for  one  to  be  too  confident.  Perhaps,  the 
most  that  can  be  claimed  for  this  theory  is  that,  practi- 
cally, it  can  do  no  harm;  that,  philosophically,  it  is  logi- 
cal; that,  physiologically,  it  is  supposable,  and  that, 
aesthetically,  the  facts  concerning  the  subject  ought  to 
develop  along  the  lines  suggested. 

In  the  last  chapter  of  this  volume  will  be  found  indi- 
cated the  connection  between  the  thought  unfolded  in  it 
and  in  the  other  volumes  of  this  series. 

The  author  wishes  to  express  his  sense  of  obligation  to 
his  colleagues,  Dr.  Allan  Marquand,  Professor  of  Archae- 
ology and  the  History  of  Art,  for  the  use  of  books  in 
his  valuable  library,  to  Dr.  Elmer  H.  Loomis,  Professor 
of  Physics,  for  his  kindly  reading  of  certain  portions  of 
the  text ; also  to  three  volumes  to  which  in  the  latter  part 
of  the  work  almost  constant  reference  seems  to  have  been 
made — Professor  Ogden  N.  Rood’s  “ Modern  Chromat- 
ics,” Professor  Joseph  Le  Conte’s  “ Sight,”  and  Professor 
Wilhelm  Von  Bezold’s  “ Theory  of  Color,”  translated 
by  S.  R.  Koehler. 

Princeton,  N.  J.,  August,  1899. 


CONTENTS. 


I. 

PAGE 

Correspondence  between  the  Elements  of  Form 

in  the  Arts  of  Sound  and  of  Sight  . 1-7 

Object  of  the  Present  Volume — Connection  between  the  Subjects 
Treated  in  it  and  the  Requirements  of  Beauty — -Similarity  of  these 
Requirements  in  the  Arts  of  Sound  and  of  Sight — Chart  of  the 
Methods  of  Art-Composition — Sounds  are  Perceived  in  Time, 
Sights  in  Space — Sounds  are  Separated  by  Silences  or  Pauses, 
Sights  by  Lines  or  Outlines — Sounds  may  Differ  in  Duration, 
Force,  Quality,  and  Pitch  ; Sights  in  Extension,  Light  and  Shade, 
and  in  Quality  and  Pitch  of  Color — Respective  Correspondences 
between  Effects  in  Sound  and  in  Sight — Combined  Influences  of 
these  Effects  as  Manifested  in  Rhythm  and  also  in  Proportion, 
as  well  as  in  Harmony,  whether  of  Sound  or  of  Sight. 

II. 

Meaning  of  Proportion  and  the  Recognition 

of  it  in  Art  and  Nature  . . . 8-19 

Proportion  as  Meaning  Measurement,  and  a Comparison  of 
Measurements,  either  Absolute  or  Relative — As  Indicating  Rela- 
tionships or  Ratios  of  Measurement,  or  Likeness  or  Equality  of 
these — Tendency  of  the  Mind  to  Make  Relative  Measurements  of 
Spaces  Illustrated — Historical  Evidences  of  the  Existence  of  this 
Tendency — Primitive  Ornamentation — Later  Ornamentation — - 
Additional  Examples  — The  Same  Tendency  as  Manifested  in 
Reproductions  of  Objects  Imitated — Proportion  as  Manifested  in 
Nature  as  a Whole  and  in  its  Parts — The  Subject  Important  and 
Complex — Its  Analogy  to  Rhythm — Ratios  Used  in  Poetry  and 
Music — In  the  Longer  Rhythmic  Divisions  of  both  Arts — Rhythmic 
Ratios  are  Represented  by  Small  Numbers,  and  thus  Rendered 

xi 


XU 


CONTENTS. 


easily  Recognizable — Same  Principle  Applicable  to  Proportion 
— Proportion  may  be  Recognized  without  a Recognition  of  the 
Exact  Ratio  Causing  it — The  Use  by  the  Greeks  of  Ratios  Repre- 
sented by  Small  Numbers. 


III. 

Effects  of  Proportion  as  Wrongly  Confounded 

WITH  THOSE  OF  PERSPECTIVE  . . . 20-31 

Difficulties  Experienced  in  Applying  Principles  of  Proportion 
— If  ever  Understood  they  can  be  Understood  to-day — Necessity, 
to  Rid  the  Subject  of  Complexity,  of  Separating  Two  Processes  in 
Perception — First,  the  Unconscious  Physical  Recognition  of  Ap- 
pearances ; Second,  the  Conscious  Mental  Measurement  of  them — 

As  Applied  to  Sounds,  the  First  Process  Determines  Effects  of 
Harmony  ; the  Second,  Effects  of  Rhythm — So  in  Sights,  not  the 
First,  but  the  Second,  Determines  Effects  of  Proportion — -This 
Results  from  the  Conscious  Measurement  of  Appearances  after 
and  as  they  have  been  Perceived,  whereas  the  Unconscious  Physical 
Process  Determines  Effects  of  Perspective — The  Two  Processes 
are  easily  Confounded,  with  Resulting  Difficulties  in  Theory  and 
Practice — The  Two  Supposed  to  have  been  Confounded  by  the 
Greeks — This  Supposition  not  wholly  Tenable— Yet  at  the  Basis 
of  Modern  Theories  which  Correlate  Proportion  to  the  Effects  of 
Musical  Pitch  upon  the  Ear,  as  do  the  Theories  of  Legh  and 
Zeising — Of  Hay,  Fergusson,  Penrose,  and  Lloyd — Impossibility 
of  any  Theoretic  or  Practical  Understanding  of  Proportion  ac- 
cording to  this  Conception  of  it. 

IV. 

Proportion  as  Based  upon  Comparisons  of  Ap- 
parent Measurements  : Straight  Lines 
and  Rectangular  Figures  . . . 32-47 

Proportion  and  Perspective  Both  to  be  Studied,  but  Separately — 
Perspective  Considers  the  Difference  between  Subjective  Effects 
and  Objective  Arrangements  Occasioning  them — Proportion  Con- 
siders Appearances,  Perspective  the  Method  of  Producing  them — 
Comparison  or  Likeness  is  the  Basis  of  Proportion — Illustrations — 
Small  Numbers  Necessary  to  the  Recognition  of  Ratios — Outlines 
Indicating  Like  Subdivisions  an  Aid  to  this  Recognition  — The 


CONTENTS. 


xiii 

PAGE 

Principle  Applicable  to  Comparisons  between  both  Rectilinear  and 
Rectangular  Measurements — Between  Adjacent  Figures  as  Wholes 
— Hay’s  Theory. 


V. 

Proportion  as  Based  upon  Comparisons  of  Meas- 
urements in  Curved  and  Complex  Figures.  48-72 
Complex  and  Irregular  Figures  Shown  to  be  in  Proportion  by 
Comparing  each  with  some  Simple  and  Regular  Figure — Regular 
Figures  as  Compared  with  Rectangles  — Importance  of  Having 
the  Rectangles  Visible — The  Choir  of  Ely  Cathedral — Illustrating 
the  Influence  of  Suggestion  in  Outlines — The  Use  of  Figures 
not  Rectangular  as  Standards  of  Comparison  between  Complex 
Figures— Aid  Afforded  by  Straight  Lines  to  the  Perception  of 
Proportion  in  Complex  Curves — Illustrations — Intimate  Connec- 
tion between  Proportion  as  thus  Manifested  and  Harmony  of 
Outline — Curved  Circles,  Ellipses,  Used  as  Standards  of  Compar- 
ison between  Complex  Figures — Application  of  this  Method  to 
the  Human  Figure. 

VI. 

Proportion  in  Landscapes,  Plants,  Animals,  and 

the  Surroundings  of  Human  Forms  . 73-84 

Outlines  and  Figures  Used  as  Standards  of  Comparison  in  Measure- 
ments— Can  be  Used  even  in  Connection  with  Accurate  Imitation 
of  Nature — Application  of  the  Principle  to  Landscape — To  Forms 
of  Vegetable  and  Animal  Life — To  the  Arranging  of  the  Sur- 
roundings of  the  Human  Form — In  Stained-Glass  Windows — 

In  Clothing — Neglect  of  this  Opportunity — The  Mind’s  Satisfac- 
tion in  a Partial  Application  of  the  Principle  — Surrounding 
Arrangements  in  Connection  with  no  Clothing. 

VII. 

Proportions  of  the  Human  Figure  Theoretic- 
ally Considered  .....  85-114 

Proportion  as  Suggested  by  Imaginary  as  well  as  Real  Lines 
Drawn  through  the  Form — Illustrated  in  the  Case  of  the  Face — 

Of  other  Parts  of  the  Body — The  Fact  that  ^Esthetic  Judgments 
of  the  Form  are  Based  on  Comparative  Measurements — The 


XIV 


CONTENTS. 


Standards  of  Measurements  Determined  by  Observation — Obser- 
vation of  Nature  Essential  to  Successful  Art — Especially  to  Repre- 
sentations of  the  Human  Form  — Opportunities  for  Observing 
this  in  Greece — Proof  that  the  Excellence  of  Greek  Sculpture  was 
Influenced  by  this  Opportunity — The  Conventionality  of  the  Face 
on  Greek  Sculpture  no  Argument  against  this — Other  Reasons 
why  the  Greek  Face  was  Conventional— The  Greek  Statues  not 
Literal  Imitations — But  their  very  Differences  Show  the  Influence 
of  the  Study  of  Nature — Connection  between  Form  and  Signifi- 
cance in  all  the  Arts  — Especially  of  those  Representing  the 
Human  Form — Physiological  Basis  for  this  View — An  Objection 
to  it — Disguising  Concealment  of  the  Form  in  Civilized  Clothing 
— Disenchanting  Exposure  of  it  in  Conventional  Art — The  Mean 
between  these  Extremes — Different  Proportions  as  Appealing  to 
Different  Tastes,  and  as  Vehicles  of  Different  Vibratory  Spiritual 
Influences. 


VIII. 

Proportions  of  the  Human  Figure  Practically 

Considered  .......  1 15-143 

Standard  of  Measurement  in  Rhythm  and  Proportion  as  Fixed 
by  Congruity — Repetition  and  Alternation — Repetition  or  Like- 
ness of  Measurements — Reason  for  Satisfaction  in  Effects  of  Pro- 
portion— Not  the  Usual  Explanation — But  not  Inconsistent  with 
the  Conceptions  of  the  Greeks — Criticism  of  Statements  with 
Reference  to  them — Difference  between  an  Apparent  and  a Real 
Measurement — Exact  Value  of  the  Statements  of  Vitruvius — How 
to  Find  the  True  Greek  Theory — Quotation  from  Vitruvius — What 
it  Implies — The  Ratios  to  be  Considered  a Result  of  Likeness — 
Measurements  of  the  Head  and  Face — The  Greek  Type  of  Face 
not  the  only  one  Manifesting  Effects  of  Proportion — Nor  are  the 
Methods  of  Subdividing  it  the  Ones  usually  Adopted — -Or  Necessary 
to  the  Recognition  of  Beauty — More  Minute  Like  Measurements  in 
the  Front  Face — In  the  Side  Face — In  the  Form  when  Fronting 
One — Effects  of  High  Civilization  on  the  Wedge-Shape  of  the 
Form — The  Lower  Limbs  from  the  Front — From  the  Side — Other 
Related  Measurements — Measurements  according  to  Curvilinear 
Standards — Similar  Circumferences  Describing  Many  Different 
Outlines — Elliptical  Figure  as  Described  about  the  Form  as  a 


CONTENTS. 


XV 


Whole — Significance  as  Represented  in  the  Form  of  a Man  and  of 
a Woman — Principles  of  Proportion  not  Creative,  but  Guides  to 
the  Selection  of  Models — Affording  Aid  in  Determining  the  Pose 
— Proportion  merely  an  Application  to  Measurements  of  the  Art- 
Methods  on  Page  3. 


IX. 

Proportion  in  Architecture  ....  144-161 

The  Study  of  Proportion  is  still  more  Essential  to  the  Architect 
than  to  the  Painter  or  Sculptor — Ways  in  which  a Building  may 
be  Given  Expression  and  Character — The  Essential  Condition 
of  Form  is  the  Grouping  of  Factors  that  in  Part  are  Alike — 
Architectural  Likeness  by  Way  of  Congruity — Of  Repetition,  Al- 
ternation, Consonance,  Interchange,  Gradation,  etc. — All  these 
Methods  may  be  Applied  to  Measurements — Ratios  of  Measure- 
ments Recognizable  when  Expressed  in  Small  Numbers — This  Fact 
as  Applied  to  an  Exterior — To  Interiors — Relative  Measurements 
Need  to  be  Apparent — Apparent  Measurements  Differ  with  Cir- 
cumstances— Effects  Produced  by  Apparent  Subdivisions  — 
Horizontal  Subdivisions  as  Indicated  by  Outlines — Vertical  Subdi- 
visions— Horizontal  as  Related  to  Vertical  Subdivisions — Influence 
of  Subdivisions  as  Counteracting  Real  Dimensions  by  Apparent 
Ones. 

X. 

Proportion  in  Architecture  (Continued)  . . 162-176 

The  Mind  Takes  Satisfaction,  not  in  Ratios,  but  in  the  Repetition 
of  Measurement  Indicated  by  them — This  Form  of  Repetition 
Illustrated — Repetitions  of  Measurements  and  Shapes  Go  together 
— Illustration  of  an  Absence  of  both  Forms  of  Repetition — Alter- 
nation of  Measurements — Consonance  as  Applied  to  Shapes — Inter- 
change as  Applied  to  Shapes — A Unique  Illustration  of  it — 
Consonance  and  Interchange  as  Applied  to  Measurement — An 
Illustration  of  them  and  of  Complication — Gradation  of  Shapes 
and  Measurements — Complement  and  Balance  of  Shapes  and 
Measurements — Proportion  an  Application  to  Measurements  of 
the  Art-Methods  Mentioned  on  Page  3, 


XVI 


CONTENTS. 


XI. 

PAGE 

Proportion  in  Greek  Architecture  . . . 177-199 

Greeks  Pre-eminent  in  Architecture — The  Secret  of  their  Methods 
of  Proportion  Involves  more  than  the  Study  of  Measurements — 

The  Mind  is  Conscious  of  Ratios  in  Proportion — It  has  Reasons 
for  Using  them — The  Reasons  of  the  Greeks  may  have  been  Dif- 
ferent from  what  we  Suppose — To  Understand  the  Reasons  we 
must  Judge  their  Buildings  as  we  do  Other  Art-Products,  by  their 
General  Effects — And  Draw  our  Conclusions  from  Many  Specimens 
— The  Authorities  Consulted  in  the  Measurements  to  be  Quoted 
in  this  Book — The  Greek  Temple  Composed  of  Different  Sets  of 
Factors,  each  Set  Plaving  the  Same  Measurements — To  Show  this 
we  are  to  Start  with  Factors  of  Small  Dimensions — SameHeightin 
the  Abacus  and  Corona  of  Horizontal  and  Raking  Cornices,  the 
Ovolo,  Cyma  Recta,  etc. — Measurements  of  these  Parts  in  Differ- 
ent Temples — Variations  and  Explanations — Like  Proportions  of 
all  the  Parts  just  Mentioned  to  the  Height  of  the  Capitals, 
and  of  both  the  Cornices  and  the  Steps — Ratios  of  1 : 2 Sustaining 
this  Statement — Of  1 : 3 — Of  2 : 3 — Like  Ratios  of  the  Parts  just 
Mentioned  to  the  Height  of  the  Architrave,  Frieze,  and  Raking 
Cornice  with  Cymatium — Also  to  Upper  Diameter  of  Shafts  and 
Width  of  Metopes— Explanations — Ratios  of  1 : 2— Of  1 : 3 — ■ 
Remarks — Like  Ratios  of  the  Parts  just  Mentioned  to  the  Height 
of  the  Entablature,  Tympanum,  and  Width  of  Upper  Inter- 
Columnation — Confirmation — Insufficiency  of  Data  with  Refer- 
ence to  the  Tympanum  and  Pediment — Like  Ratios  of  the  LI eight 
of  Entablature  and  Pediment  Spaces,  Differently  Divided,  to  the 
Height  of  Column-Space — The  Different  Methods  of  Dividing 
these  Gave  Opportunity  for  Originality  Exercised  in  Conformity 
to  Law. 


XII. 

The  Larger  Divisions  of  the  Front  of  the 

Doric  Temple  ......  200-214 

The  Column-Space  and  the  Method  of  Principality — Proportion 
on  the  Flanks  of  Height  of  Columns  to  the  Entablature — Variety 
of  Exact  Proportions  on  the  Front  might  Arise  from  a Desire  to 
Have  Similar  Apparent  Proportions— Difficulty  of  Determining  the 


CONTENTS. 


XVU 


Line  of  Separation  between  the  Tympanum,  Entablature,  and 
Column-Spaces — Illustrated  in  the  Temple  at  H2gina — How  its 
Tympanum  and  Entablature  each  can  be  Made  to  be  to  Columns 
as  i : 3 — How  Pediment  and  Entablature,  Including  Capital,  each 
can  be  Made  to  be  to  Shaft  as  i : 2 — How  Rectangles  of  Front 
in  Foundation,  Columns,  Entablature,  Pediment,  etc.,  are  all  in 
Proportion — Triangle  of  both  Tympanum  and  Pediment  are  in 
Proportion  to  Spaces  under  them — These  Arrangements  Illustrate 
the  Complexity  of  Harmony,  but  are  Analogous  to  those  of  Rhythm, 
not  Pitch — Illustrated  from  Temple  at  Bassee — Entablature,  Pedi- 
ment, and  Columns — Proportions  of  the  Rectangles  Formed  by  the 
Front  Spaces — Temples  in  which  the  Abacus  is  Treated  as  Part 
of  the  Entablature  Space — Proportions  of  the  Rectangles  of  the 
Front  in  Propylaea  and  the  Theseum— The  Parthenon  at  the  Be- 
ginning of  a Transition — Departure  in  it  from  Former  Methods — 
How  these,  nevertheless,  Conform  to  the  Principles  here  Unfolded 
— Other  Subordinate  and  Complementary  Proportions — All  Tend- 
ing to  Produce  General  Harmony  of  Effect. 


XIII. 

Other  Greek  Architectural  Measurements 

and  General  Conclusions  ....  215-228 

Unusual  Size  of  the  Tympanum  of  the  Parthenon — Reasons  for 
this — Proportions  of  the  Rectangles  of  the  Front  of  the  Parthenon 
— Same  Principles  Revealed  in  the  Measurements  of  Other 
Temples — Exact  Squares  Formed  by  the  Width  and  Height  of 
Three  Adjacent  Columns  in  Many  Temples — Proportion  between 
the  Diameters  and  Heights  of  Many  Columns — Measurements 
from  Twenty-three  Doric  Temples  Verifying  the  hitherto  Unveri- 
fied Statements  in  Chapters  X.  and  XI. — Why  the  Doric  Temples 
are  Chosen  for  Illustrations — After  Experiment  had  Determined 
the  Laws  of  Proportion,  Art  Imitated  and  Degenerated — Because 
Artists  no  longer  Followed  out  the  Natural  and  Instinctive  Art 
Tendency  Founded  upon  Comparison  — This  Tendency  Appar- 
ent in  that  which  Originated  the  Gothic  and  Renaissance  Styles — 

No  Great  Architecture  without  it — Possibilities  of  Architecture 
not  Exhausted  but  must  be  Developed  from  the  Principle  of 
Comparison. 


CONTENTS. 


xviii 


XIV. 

PAGE 

Harmony  of  Outline  : Perspective  . . . 229-253 

Outlines  and  Colors,  the  Respective  Analogues  of  Words  and  Tones 
— Form-Harmony  is  less  Essential  than  Significant  Representa- 
tion, yet  Important — In  Poetry  Harmony  is  Owing  to  Apparent 
Like  Effects  as  in  Alliteration,  etc.,  and  also  to  Subtle  Effects 
Adapted  to  Ease  of  Auditory  Action — Analogous  Conditions  in 
Arts  of  Outline  : The  Perspective  and  Circumspective — Perspective 
Relates  all  Objects  to  a Centre  of  the  Field  of  Sight : Lines,  Direc- 
ted toward  this  Centre,  Converge — Appearance  of  Horizontal 
Lines — Of  Vertical  Lines — Both  Lines  as  Represented  in  Paint- 
ing and  Architecture — Optical  Illusions  in  Triangles — In  Horizon- 
tal with  Crossing  Vertical  Lines — Exact  Explanation  of  these 
Illusions  not  as  Important  as  to  Recognize  that  they  Exist — An- 
alogy Drawn  from  Effects  of  Color  Remote  and  Near — Failure 
in  our  Time  to  Recognize  the  Fact  as  Applied  in  Architecture — 

A Building  was  once  Judged  by  its  General  Effect  as  Seen  from  a 
Distance — Proof  of  this  Furnished  by  Discoveries  in  Egypt  and 
Greece  by  Pennethorne,  Hofer,  Schaubert,  and  Penrose — By 
Goodyear — His  Special  and  General  Contribution  to  the  Subject — 
Some  Measurements  of  Penrose — To  be  Interpreted  as  Related  to 
Perspective,  not  to  Proportion — Differences  in  Measurement  Ac- 
cord with  this  Interpretation — Greek  Architects  Experimented 
with  their  Products  as  Artists  do  in  other  Arts. 

XV. 

Harmony  of  Outline  : Perspective  as  Deter- 
mining Entasis  and  Irregularity  in 
Greek  Architecture  .....  254-265 

Upward  Curves  in  apparently  Plorizontal  Architectural  Lines 
Ascribed  to  Effects  of  Pediment — To  the  Formation  of  the  Eye — 

An  Explanation  of  Vitruvius — Ascribed  to  a Desire  to  Increase 
Apparent  Size — To  a Desire  to  Represent  Relationship  to  Other 
Lines — Forward  Leaning  of  apparently  Perpendicular  Lines — In- 
ward Leaning  and  Tapering  of  the  Columns — Designed  Physically 
to  Meet  Requirements  of  the  Eye  and  Artistically  to  Suggest 
Height — The  Same  is  True  of  the  Outward  and  Inward  Curving 
of  the  Column’s  Sides — Laws  of  Vitruvius  with  Reference  to 


CONTENTS. 


XIX 


Columns — Differences  in  the  Measurements  of  Different  Greek 
Columns — Difference  between  the  Greek  and  Roman  use  of  Prin- 
ciples— Columns  and  Spaces  at  the  Corners  of  Colonnades — Sizes 
of  Columns  as  Determined  by  their  Position  Exterior  and  In- 
terior— General  Conclusion. 


XVI. 

Harmony  of  Outline  : Binocular  Vision  . . 266-295 

Curvature — The  Field  of  Vision  for  both  Eyes  not  the  Same — The 
Horopter  which  both  Eyes  See — At  either  Side  of  the  Horopter 
Something  else  Seen  by  but  One  Eye : Its  Influence  on  the 
Recognition  of  Relief  in  Form— This  Fact  as  Developed  in 
Stereoscopy — Other  Illustrations— Perception  of  Relief  at  the  Sides 
of  an  Object  through  Unconscious  though  Constant  Movement  of 
the  Eyes — As  a Result  of  no  Movement — Seeing  the  Sides  of  an 
Object  Important  to  Gaining  a Conception  of  its  Form — Shape  of 
the  Eyes’  Field  of  Sight,  for  each  Eye  and  for  both  Eyes — The 
Horizontal  Shape  Seen  with  the  Least  Effort  is  Rounded  Back- 
ward— The  Perpendicular  Shape  is  Elliptical  — Convergence  of 
Axis,  and  a Lack  of  it  as  Applied  to  Near  and  Distant  and  to 
Many  and  Few  Details — Practical  Experiments  Evincing  Ease 
of  Perception  of  all  Outlines  in  an  Elliptical  Shape — To  Per- 
ceive Outlines  of  this  Shape,  no  Conscious  Movement  of  the  Eye’s 
Lens  is  Necessary — Therefore  they  Realize  the  Condition  Re- 
quired by  Visual  Rest,  Enjoyment,  Beauty — This  Fact  may  Ex- 
plain the  Use  of  the  Ellipse  in  Art — The  Ellipse  in  General — In 
Vases,  Leaves,  Birds,  Animals,  Fishes — Human  Form — -Its  Like 
Curves  are  Accommodated  to  the  Least  Expenditure  of  Visual 
Effort — The  General  Method  through  which,  when  the  Eye’s  Axis 
Changes,  we  can  Look  from  One  to  Another  Line  with  the  Least 
Visual  Effort. 


XVII. 

Artistic  Coloring  as  Influenced  by  Scientific 

Methods 296-308 

Imitative  and  Decorative  Use  of  Color — The  Two  Connected 
— Scientific  Study  of  Color  Important— Art  can  Advance  beyond 
the  Discoveries  of  Science — Yet  in  every  Age  is  Helped  by  them 


XX 


CONTENTS. 


— Artistic  Invention  as  Related  to  Scientific  Investigation  of 
Effects  of  Color — Illustrated  from  History  of  Greek  Painting — 
Roman  — Christian  — Italian  — Spanish  and  Dutch — English — 
French — German — Modern — Need  of  Learning  from  Experience 
and  Experiment. 

XVIII. 

Effects  of  Color  as  Discovered  by  Scientific 

Experiments  ......  309-324 

Newton’s  Discovery  of  the  Colors  of  the  Spectrum — They  are 
Contained  only  in  White  Light — The  Diversity  and  Brilliancy  of 
the  Spectrum’s  Colors  Dependent  on  the  Amount  and  Intensity  of 
the  Light — Brightness  and  White  Making  all  Colors  Pale  ; Dark- 
ness and  Black  Making  them  the  Opposite — Names  of  the  Chief 
Colors — The  Terms:  Hues,  Full,  High,  Dark,  Light,  Pale, 
Broken,  Shades,  Tints,  Tone,  Local,  Positive,  Neutral,  Warm, 
Cold,  Primary,  Secondary — Colors  Transmit  and  Reflect  Rays  of 
Like  Color  with  themselves — Practical  Bearing  of  this  upon  the 
Kind  of  Light  with  which  Objects  are  Illumined,  Lamps,  Sun,  etc. 

— Shows  why  Colors  are  most  Vivid  when  Illumined  by  Light  of 
their  own  Color — Why  White  Objects  Reflect  the  Color  Illumin- 
ing them — What  are  the  Actual  Colors  of  Nature — Of  Foliage — 

Of  Water — Of  the  Atmosphere — Of  Objects  in  External  Nature 
in  Light  or  Shade,  when  the  Sun  is  on  the  Horizon — Especially 
at  a Distance — When  the  Sun  is  in  the  Zenith — Colors  of  the  Same 
Objects  in  Cloudy  Weather  ; the  Terms  Cold  and  Warm — Effects 
of  Light  and  Shade  within  Doors — Cold  and  Warm  Colors  in  the 
Representation  of  Distance — These  Effects  Dependent  on  the 
Degrees  of  Light — Difference  of  Opinion  with  Reference  to  Cer- 
tain Deductions  Made  from  Acknowledged  Facts  of  Aerial  Per- 
spective— The  Apparent  Truth  with  Reference  to  the  Subject. 

XIX. 

Basis  of  Color-Harmony 325-336 

The  Tendency  in  Natural  Color  for  Like  to  Go  with  Like  in 
Analogy  with  the  Same  Tendency  in  Natural  Language — Differ- 
ences of  Opinion  Regarding  the  Essential  Requirements  of  Color- 
Harmony — Some  Truth  in  all  these  Opinions,  but  only  so  far  as 
Certain  Principles  are  Fulfilled — Those  of  Unity,  Variety,  Com- 


CONTENTS. 


XXI 


plexity,  Order,  Confusion,  Counteraction,  Grouping — Like  with 
Like  in  the  Colors  of  Nature,  is  the  Basis  for  the  Same  Arrange- 
ment by  Way  of  Comparison  and  Contrast — Colors  Called  the 
Contrasting  or  Complementary  Colors  not  All  that  really  Contrast 
— The  Complementary  Colors — What  they  are  as  Determined  by 
Dividing  the  Rays  of  Light — As  formerly  Determined  by  Mixing 
Pigments — Proof  of  the  Erroneousness  of  the  Latter  Method — 

Von  Bezold’s  Color  Chart — As  One  Complementary  Becomes 
Brighter,  the  Other  Becomes  Darker — Wide  Differences  in  the 
Complementaries  of  Different  Shades  of  Green. 

XX. 

Physical  and  Physiological  Correspondences 

between  Harmony  in  Music  and  Painting.  337-351 

Study  of  Color-Effects  in  the  Eye  itself — Not  as  far  Advanced  as 
the  Study  of  Sound-Effects  in  the  Ear  ; Facts  Known  with 
Reference  to  the  Effects  of  Amplitude  and  Rate  of  Sound-Waves 
— Of  their  Form — Compound  Waves — Determining  Quality — 
Partial  Tones — Their  Influence  upon  Harmony,  Simultaneous 
and  Successive — Correlation  of  Rhythm  and  Harmony  ; the  Lat- 
ter’s Physiological  Effect— Foster’s  Explanation — Correspondences 
between  Vibratory  Effects  in  the  Ear  and  in  the  Eye — Differences 
between  them — Inferences  from  the  Minuteness  of  Color- Waves — 
Two  Main  Questions  Involved  in  the  Discussion  of  Color- 
Harmony. 

XXI. 

General  Effects  of  Color  in  Paintings  Consid- 
ered as  Wholes  ......  352-369 

Artistic  Harmony  not  Imitated  from  Nature — Field-Theory  with 
Reference  to  the  Method  of  Securing  it — Physiological  Objection 
to  it — Psychological — -Principality,  Subordination:  Tone — Har- 
mony, whether  Due  to  Similarity,  as  in  Tone,  or  to  Variety,  an 
Exemplification  of  Similar  Physiological  Requirements — Analogy 
from  Music  and  the  Key-Note — Balance  and  Organic  Form — Their 
Effects  both  Psychical  and  Physiological — Congruity  as  Represent- 
ing Conceptions  and  Conditions — Incongruity,  Comprehensive- 
ness, Central-Point,  Setting,  and  Parallelism  — Symmetry — 


XXII 


CONTENTS. 


Repetition — Alteration,  Alternation — Massing,  Breadth,  or  Chi- 
aroscuro— Its  Relation  to  Principality  and  Balance — And  Other 
Methods — Interspersion,  Complication,  and  Continuity. 

XXII. 

Special  Effects  of  Colors  when  Placed  Side  by 

Side.  ........  370-388 

Consonance — Importance  of  this  Subject — Colors  Placed  Side  by 
Side  Produce  Subjective  Effects  in  the  Eye — Successive  Contrast 
or  After-Image  of  Complementary  Colors  Following  Colors  sud- 
denly Obscured — A Similar  Phenomenon  among  Sounds — Ex- 
planation of  Differences  between  the  Phenomena  — Ordinary 
Explanation  of  the  After-Images — Simultaneous  Contrasts  as  in 
Shadows — Suggested  Insufficiency  of  Reasons  ordinarily  Given  for 
Successive  and  Simultaneous  Contrast  — Suggestions  with  Re- 
ference to  the  Perception  of  Color — Nothing  in  the  Organism 
to  Throw  Doubt  upon  these  Suggestions — The  Principle  Involved 
Explains  the  Main  Difference  between  Successive  and  Simultaneous 
Contrast — Colors  Impart  about  them  Tints  of  their  Complemen- 
taries — These  Effects  on  Light  and  Shade  or  on  Light  and  Dark 
Neutral  Surfaces  as  Produced  by  Warm  and  Cold  Colors — By 
Different  Tints  and  Shades — Same  Effects  as  Produced  on  Colored 
Surfaces — Three  Ways  of  Using  Contrast  to  Relieve  Objects  from 
their  Background. 


XXIII. 

Color-Scales  .......  389-405 

Object  of  this  Chapter — Colors  can  be  Used  together  that  Differ 
either  Slightly  or  Greatly — Theory  that  Two,  Three,  or  More  can 
be  Used  together  if  they  Make  White — Theory  Based  on  Con- 
struction of  Color-Scales  : Von  Bezold’s  of  Twelve  Colors — Rood’s 
Summary  of  Combinations  of  Colors  Founded  on  Experience — 
Combinations  Determined  as  in  Musical  Harmony  by  Ratios  be- 
tween the  Numbers  of  Vibrations  a Second  Causing  the  Colors — 

All  the  Colors  can  Represent  only  the  Ratios  Possible  to  a Single 
Scale — Compensating  Possibility  of  Variety  in  each  Color — Cor- 
respondences Need  to  be  Found  only  between  the  Ratios  Under- 
lying the  Harmonic  Notes  and  the  Harmonic  Colors — The  Ratio 


CONTENTS. 


Xxiii 

PAGE 

Expressive  of  the  Two  Chief  Harmonics  of  Music  aside  from  that 
of  the  Octave,  which  has  no  Analogue  in  Color — The  Same  Ratio 
as  Applied  to  Color — The  Tonic  and  Dominant  Harmonize  all 
the  Notes  of  the  Scale  as  the  Two  Complementaries  Contain 
all  the  Colors  of  the  Spectrum — The  Tonic  and  Dominant  Represent 
the  Same  Ratios  as  the  Complementaries — Reasons  for  Apparent 
Exceptions — Ratios  Expressive  of  the  Three  Harmonics  in  the 
Major  Triad  of  Music — Same  Ratios  Applied  to  Triads  of  Colors 
— Recapitulation — A Fourth  Color  would  Naturally  Correspond  to 
the  Seventh  in  Music,  a Result  Approximating  that  Reached  by 
Von  Bezold — The  Reason  why  Notes  and  Colors  thus  Related 
Satisfy  the  Senses — Similarity  of  Method  in  Determining  Con- 
sonance either  in  Sound  or  Color. 


XXIV. 

Additional  Art-Methods  Causing  Color-Har- 
mony ........  406-412 

Dissonance  and  Interchange — Criticism  by  Sir  Joshua  Reynolds — 
Gradation — Suggested  by  Nature — Physiological  Explanation  of — 
Abruptness — Transition  and  Progress. 


XXV. 

The  Foregoing  Principles  as  Applied  to  Decora- 
tive Painting  ......  413-418 

Differences  between  the  Use  of  Color  in  Pictorial  and  Decora- 
tive Art — Differences  between  Classes  of  Forms  to  which  Colors 
are  Applied  and  Classes  of  Like  Colors  that  are  Applied  to  Like 
Forms — Monochromatic  and  Polychromatic  Decoration — Color  on 
the  Exteriors  of  Buildings — Possibility  of  New  Styles  of  Architec- 
ture in  our  Age — Modern  Development  of  Mineral  Resources  and 
Facilities  of  Transportation  and  their  Influence  on  the  Shapes  of 
Buildings — But  Especially  on  their  Sizes  and  their  Colors  as  Pro- 
duced both  by  Pigments  and  by  the  Materials  Used — Errors  to  be 
Avoided  in  Attempting  Originality,  but  Possibility  of  Success. 


XXIV 


CONTENTS. 


XXVI. 

PAGE 

Recapitulation  of  Results  Reached  in  these 

Volumes  on  Comparative  ^Esthetics  . 419-439 

Introductory  Statement — Examination  of  Facts  and  Opinions  in 
“Art  in  Theory” — Method  Adopted  in  Volumes  Following  it  — 

In  “The  Representative  Significance  of  Form” — Art  Developed 
from  Natural  Forms  of  Expression — The  Methods  of  their  De- 
velopment— Elements  of  Representation  in  Arts  of  Sound,  as 
Analyzed  in  “ Poetry  as  a Representative  Art  ” and  in  “ Music  as 
a Representative  Art”  — As  Combined,  according  to  the  Same 
Essays,  in  Poems  and  Musical  Compositions  Considered  as  Wholes 
— Elements  of  Representation,  as  Analyzed  in  “ Painting,  Sculp- 
ture, and  Architecture  as  Representative  Arts” — As  Combined, 
according  to  the  Same  Volume,  in  Paintings,  Statues,  and  Build- 
ings Considered  as  Wholes — Form  in  General  as  Treated  in  “ The 
Genesis  of  Art-Form  ” — Form  in  Particular  as  Treated  in 
“Rhythm  and  Harmony  in  Poetry  and  Music,”  and  in  “Pro- 
portion and  Harmony  of  Line  and  Color  in  Painting,  Sculpture, 
and  Architecture  ” — This  Series  of  Volumes  Traces  All  Art- 
Developments,  whether  of  Significance  or  Form,  to  a Single  Prin- 
ciple— This  Done  with  a Practical  as  well  as  Philosophic  Aim — 

The  Acknowledgment  of  No  Standards  Leads  either  to  Imitation 
or  Eccentricity  in  Production  and  in  Critical  Judgment — The 
Possibility  of  Finding  Standards — These  Need  not  Interfere  with 
Originality— Necessity  for  the  Study  and  Knowledge  of  Standards 
in  our  own  Age  and  Country — Unavoidable  Limitations  in  a 
Philosophic  and  Technical  Treatment  of  the  Kind  Attempted  in 
these  Volumes. 


Index 


• 441-459 


ILLUSTRATIONS. 


PAGE 

1.  The  Vitruvian  Scroll 12 

From  photograph  of  an  engraving.  Mentioned  on  pages  12,  40. 

2.  The  Greek  Fret 12 

From  photograph  of  an  engraving.  Mentioned  on  pages  12,  40, 

3.  Triglyphs  and  Metopes,  from  a Greek  Temple  . . 12 

From  photograph  of  an  engraving.  Mentioned  on  pages  12,  40,  168. 

4.  Illustration  of  the  Formation  of  an  Image  on  the  Retina,  22 

From  Le  Conte’s  44  Sight.”  Mentioned  on  pages  22,  23,  234. 

5.  The  Cavity  of  the  Eye 22 

From  the  same.  Mentioned  on  pages  21,  22. 

6.  A Maori  Festival,  New  Zealand 33 

From  Cassell’s  4‘  Isles  of  the  Pacific.”  Mentioned  on  pages  40, 162,  174. 

7.  Kaffir  Station,  Africa 34 

From  Cassell’s  44  Races  of  Mankind.”  Mentioned  on  pages  40,  162. 

8.  Type  of  an  Assyrian  Square 35 

From  Cassell’s  Magazine  of  Art.  Mentioned  on  pages  40,  43,  44,  162. 

9.  Mediaeval  Castle 36 

From  Cassell’s  44  Land  of  Temples.”  Mentioned  on  pages  40,  145,  162. 

10.  Temple  of  Theseus,  Athens 36 

From  Liibke’s  44  History  of  Art.”  Mentioned  on  pages  40,  44,  116,  156, 

163,  164,  168,  170,  175,  188,  189,  193,  196,  201,  210,  211,  218,  219,  220,  22i,  224, 

252. 

11.  St.  Stephen’s  Caen,  Normandy 37 

From  Fergusson’s  44  History  of  Architecture.”  Mentioned  on  pages  42, 

44,  154,  163,  166,  170,  175,  226. 

12.  Canterbury  Cathedral,  from  Southwest  ....  38 

From  a photograph.  Mentioned  on  pages  42,  163,  175,  226. 

13.  Central  Congregational  Church,  Boston,  Mass.  . . 39 

From  Cassell’s  44  The  World,  its  Cities  and  its  People.”  Mentioned  on 
page  42. 


XXV 


XXVI 


ILL  USTRA  TIONS. 


PAGB 

14.  Willesden  Church,  near  London,  England  ...  40 

From  Cassell’s  44  Greater  London. ” Mentioned  on  pages  42,  154. 

15.  Chichester  Cathedral,  England 41 

From  Cassell’s  44  Our  Own  Country.”  Mentioned  on  pages  42,  43,  158, 

163,  165. 

16.  Lines  in  Proportion 42 

From  a drawing.  Mentioned  on  pages  42,  43. 

17.  Lines  Subdivided  to  Indicate  Proportion  ....  43 

From  the  same.  Mentioned  on  page  43. 

18.  Figures  with  Lines  Subdivided  to  Indicate  Proportion  . 44 

From  the  same.  Mentioned  on  pages  44,  263. 

19.  Rectangles  in  Proportion 45 

From  the  same.  Mentioned  on  page  45. 

20.  Hay’s  Method  of  Determining  Proportional  Relations 

of  Rectangles 45 

From  D.  R.  Hay’s  44  Science  of  Beauty  and  Laws  of  Geometric  Propor- 
tion.” Mentioned  on  page  46. 

21.  Hay’s  Rectangles  Corresponding  to  the  Musical  Scale  . 46 

From  the  same.  Mentioned  on  page  47. 

22.  Figures  Related  Because  Inscribable  in  the  Same  Square,  49 

From  drawings.  Mentioned  on  page  49. 

23.  Figures  Related  Because  Inscribable  in  the  Same  Rect- 

angle   49 

From  the  same.  Mentioned  on  page  49. 

24.  Figures  Related  Because  Inscribable  in  the  Same  or  a 

Related  Figure 49 

From  the  same.  Mentioned  on  pages  49,  50. 

25.  Figures  Related  Because  Inscribable  in  Figures  in  Pro- 

portion   50 

From  the  same.  Mentioned  on  pages  50,  51. 

26.  Relationship  of  Figures,  as  Indicated  and  as  not  In- 

dicated   50 

From  the  same.  Mentioned  on  page  50. 

27.  Chateau  de  Randau,  Vichy,  France 51 

From  a photograph.  Mentioned  on  pages  51,  149,  164,  166. 

28.  Chenonceau  Chateau,  France 53 

From  Liibke’s  44  History  of  Art.”  Mentioned  on  pages  52,  166. 

29.  Walker  Museum,  Chicago  University 54 

From  the  Cosmopolitan  Magazine , Mentioned  on  page  52, 


ILL  USTRA  TIONS. 


XXV11 


PAGE 

30.  Choir  of  Ely  Cathedral,  England 55 

From  Fergusson’s  “ History  of  Architecture.”  Mentioned  on  pages  52, 

56,  57,  163,  166. 

31.  Lines  and  Curves  Indicating  Proportions  of  a Human 

Form.  Front  View 57 

Drawn  about  an  illustration  in  Putnam’s  “Art  Hand-Book  of  Figure 
Drawing.”  Mentioned  on  pages  15,  58,  59,  69,  72,  85,  87,  118,  120,  130,  131, 

13S,  137.  I38.  29°i  29H  295- 

32.  Back  View  of  the  Same 58 

Drawn  about  the  same.  Mentioned  on  pages  15,  58,  59,  69,  85,  87,  118, 

120,  130,  131,  135,  137,  290,  295. 

33.  Curve  Exemplifying  Gradation 60 

From  Ruskin’s  “ Modem  Painters.”  Mentioned  on  pages  59,  69,  294. 

34.  Curve  Exemplifying  Gradation 61 

From  the  same.  Mentioned  on  pages  59,  69,  294. 

35.  Circles  Drawn  about  a Man’s  Form.  Side  View  . . 70 

Added  to  an  illustration  in  Putnam’s  ” Art  Hand-Book  of  Figure  Draw- 
ing.” Mentioned  on  pages  15,  59,  69,  87,  134,  135,  I4r,  290,  294,  295. 

36.  Circles  Drawn  about  Form  of  D.  R.  Hay’s  Ideal  Man  . 71 

Added  to  illustration  in  Hay’s  “Geometric  Beauty  of  the  Human  Fig- 
ure.” Mentioned  on  pages  15,  59,  69,  72,  87,  133,  134,  135,  295. 

37.  Circles  Drawn  about  Form  of  Hay’s  Ideal  Woman  . 72 

Added  to  an  illustration  in  the  same.  Mentioned  on  pages  59,  69,  72, 

87,  134,  29s. 

38.  The  Canal,  Corot 75 

From  a photograph.  Mentioned  on  pages  74-77,  363,  365,  369. 

39.  Radiation  in  Natural  Forms 78 

From  Ruskin’s  “ Elements  of  Drawing.”  Mentioned  on  pages  78,  288. 

40.  Stained  Glass  of  the  Fourteenth  Century  ...  79 

From  Cassell’s  Magazine  of  Art . Mentioned  on  page  79. 

41.  Costumes  Dividing  the  Human  Form  Proportionately  . 80 

From  a drawing  by  C.  C.  Rosenkranz.  Mentioned  on  pages  81,  82. 

42.  Costumes  not  Dividing  the  Human  Form  Proportionately,  8i 

From  the  same.  Mentioned  on  pages  81,  82. 

43.  A New  Guinea  Chief 82 

From  Cassell’s  “ Picturesque  Australia.”  Mentioned  on  pages  83,  130, 

I3I>  I32.  133,  14I* 

44.  The  Apollo  Belvedere 84 

From  Liibke’s  “ History  of  Art,”  Mentioned  on  pages  83,  84,  98,  99, 102, 
i?i>  i32<  I4I- 


XXVlii  ILLUSTRATIONS. 

PAGE 

45.  Front  Face  Divided  Proportionately  by  Lines  . . 86 

Drawn  over  an  illustration  from  Putnam’s  “ Art  Hand-Book.”  Men- 
tioned on  pages  15,  59,  86,  87,  105,  120,  125,  126,  128,  129,  134,  141,  295. 

46.  Ear  and  Eye  Proportionately  Divided  by  Straight  Lines,  86 

From  the  same.  Mentioned  on  pages  87,  141. 

47.  Venus  de’  Medici,  Statue  of 92 

From  Mitchell’s  14  History  of  Sculpture.”  Mentioned  on  pages  92,  97, 

99,  102,  141. 

48.  Farnese  Hercules,  Statue  of 94 

From  the  same.  Mentioned  on  page  97. 

49.  Diadumenos,  by  Polycleitus,  Statue  of  . . .95 

From  Cassell’s  44  Greek  Archaeology.”  Mentioned  on  pages  97,  132,  141. 

50.  Discobolus  or  Quoit  Thrower,  by  Myron,  Statue  of  . 96 

From  Turner’s  44  Short  History  of  Art.”  Mentioned  on  pages  97,  141. 

51.  Pallas  of  Velletri,  from  the  Louvre,  Paris  ...  97 

From  Viardot’s  44  Wonders  of  Sculpture.”  Mentioned  on  page  97. 

52.  Theseus  of  the  Parthenon,  Statue  of  ....  98 

From  Abbott’s  44  Pericles.”  Mentioned  on  pages  97,  141. 

53.  Faun,  by  Praxiteles,  Statue  of 99 

From  Liibke’s  44  History  of  Art.”  Mentioned  on  pages  97,  99,  141. 

54.  Hermes,  by  Praxiteles,  Statue  of ioo 

From  Cassell’s  44  Gods  of  Olympus.”  Mentioned  on  pages  97,  99,  102, 

132,  14  »• 

55.  Group  of  Niobe,  Sculpture ioi 

From  Muller’s  44  Denkmaler  der  Alten  Kunst.”  Mentioned  on  pages  59,  98. 

56.  Meleagros,  Statue  in  the  Vatican 102 

From  Cassell’s  44  Gods  of  Olympus.”  Mentioned  on  pages  99,  141. 

57.  Ganymede,  after  Leochares,  Statue  of  ...  103 

From  the  same.  Mentioned  on  pages  99, 132,  141. 

58.  Apollo  Sauroctonos,  by  Praxiteles,  Statue  of  . . 104 

From  Cassell’s  44  Gods  of  Olympus.”  Mentioned  on  pages  99,  141. 

59.  Venus  Ascribed  to  Style  of  Praxiteles,  Statue  of  . 105 

From  Cassell’s  Magazine  of  A rt , Mentioned  on  pages  99,  102,  141. 

60.  Mephistopheles  as  Depicted  in  Art 106 

From  Well’s  44  New  Physiognomy.”  Mentioned  on  page  106. 

61.  Contempt  and  Anger  as  Depicted  in  the  Countenance  . 106 

From  the  same.  Mentioned  on  page  106. 

62.  Whole  Human  Form  as  Related  to  the  Circle  . . 121 

From  Cassell’s  Magazine  of  Art.  Mentioned  on  pages  15,  59,  121,  130, 

132,  133. 


ILL  US  TLA  TIONS. 


XXIX 


63.  Whole  Human  Form  as  Related  to  the  Square 

From  the  same.  Mentioned  on  pages  15,  sg.  122,  130,  131,  141. 

64.  Face  Proportionately  Divided  by  Straight  Lines  . 

Drawn  over  a photograph  in  the  Dramatic  Mirror.  Mentioned  on 
pages  116,  126,  127,  128,  130. 

65.  Face  Proportionately  Divided  by  Straight  Lines  . 

From  the  same.  Mentioned  on  pages  116,  126,  127,  128. 

66.  Face  Proportionately  Divided  by  Straight  Lines  . 

From  the  same.  Mentioned  on  pages  116,  126,  127,  128. 

67.  Face  Proportionately  Divided  by  Straight  Lines  . 

From  the  same.  Mentioned  on  pages  116,  126,  127,  128. 

68.  Face  Proportionately  Divided  by  Straight  Lines  . 

From  the  same.  Mentioned  on  pages  116,  126,  127, 128,  130. 

69.  Side  Face  Divided  by  Lines 

Drawn  over  illustration  in  Putnam’s  44  Art  Hand-Book  of  Figure  Draw- 
ing.” Mentioned  on  pages  15,  59,  126,  128,  129,  130,  135. 

70.  Leg  and  Foot  

From  Duval’s  44  Artistic  Anatomy.”  Mentioned  on  pages  132,  133. 

71.  Clothing  Proportional  in  Parts 

From  a drawing  by  C.  C.  Rosenkranz.  Mentioned  on  pages  82,  130,  133. 

72.  Woman’s  Form  Enclosed  Between  Circles 

From  a drawing.  Mentioned  on  pages  59,  138,  270,  291,  295. 

73.  Man’s  Form  Enclosed  Between  Circles  . 

Drawn  about  D.  R.  Hay’s  ideal  man  in  44  Geometric  Beauty  of  the 
Human  Figure.”  Mentioned  on  pages  15,  59,  72,  87,  135,  137,  138,  290,  291 
2Q5- 

74.  Woman’s  Form  Enclosed  in  Like  Circles  . 

Drawn  about  a model-figure  in  the  same,  prepared  for  D.  R.  Hay. 
Mentioned  on  pages  15,  59,  72,  87,  135,  138,  290,  295. 

75.  Figure  from  Nausica,  by  E.  J.  Poynter  . 

From  Cassell’s  44  History  of  Art.”  Mentioned  on  pages  59,  133,  141,  369. 

76.  University  at  Sydney,  Australia 

From  Cassell’s  44  Picturesque  Australia.”  Mentioned  on  pages  146,  158, 
163,  165,  175,  226. 

77.  Pavilion  of  Richelieu,  Louvre,  Paris  .... 

From  Cassell’s  “The  World,  its  Cities  and  Peoples.”  Mentioned  on 
pages  42,  44,  149,  152,  154,  158,  160,  162,  163,  175. 

78.  Arch  of  Septimius  Severus 

From  Fergusson’s  44  History  of  Architecture.”  Mentioned  on  pages  152, 

163, 175. 


PAGE 

122 

126 

126 

127 

127 

127 

128 

133 

134 

I36 

137 

139 

142 

147 

150 

152 


XXX 


ILL  US  TRA  RIO  NS. 


PAGE 

79.  Arch  of  Augustus  at  Aosta 153 

From  a drawing.  Mentioned  on  pages  152,  163. 

80.  Temple  of  Themis,  at  Rhamnus 153 

From  a drawing.  Mentioned  on  pages  152,  154,  163,  164, 168,  175. 

81.  Cologne  Cathedral,  Facade 155 

From  a photograph.  Mentioned  on  pages  42,  44,  153,  154,  156,  157,  160, 

163,  165,  175,  226,  236,  237. 

82.  St.  Sulpice,  Paris 156 

From  Fergusson’s  11  History  of  Modern  Architecture.”  Mentioned  on 
pages  42,  43,  44,  154,  158,  160,  161,  166,  175. 

83.  St.  Sulpice  Modified 157 

Mentioned  on  page  161. 

84.  St.  Sulpice  Modified 159 

Mentioned  on  page  161. 

85.  An  American  Church 163 

From  Fergusson’s  44  History  of  Modern  Architecture.”  Mentioned  on 
pages  164,  1 66. 

86.  Opera  House,  Paris 167 

From  the  same.  Mentioned  on  pages  15,  166,  167,  170,  175,  226. 

87.  Saint  Etienne  du  Mont,  Paris 169 

From  Cassell’s  “Paris.”  Mentioned  on  pages  167,  168. 

88.  German  Spire  at  Kuttenberg 171 

From  Fergusson’s  44  History  of  Modern  Architecture.”  Mentioned  on 
page  172. 

89.  Steeple  of  Bow  Church,  London 171 

From  the  same.  Mentioned  on  page  172. 

90.  Street  and  Belfry  at  Ghent 172 

From  Cassell’s  44  The  World,  its  Cities  and  Peoples.”  Mentioned  on 
page  172. 

91.  Tower  of  Boris,  Kremlin,  Moscow 173 

From  a drawing.  Mentioned  on  pages  172,  173. 

92.  Dome  of  Chiava valle  in  Italy 174 

From  a drawing.  Mentioned  on  page  173. 

93.  Column  and  Entablature  of  the  Temple  at  tEgina  . 182 

From  a drawing.  Mentioned  on  pages  183,  185,  187,  188,  191,  192,  203,  219. 

94.  Greek  Doric  Temple  of  ^Egina,  Facade  . . . .183 

From  Fergusson’s  44  History  of  Architecture.”  Mentioned  on  pages  42, 

170,  183,  185,  186,  187,  188,  189,  191,  192,  196,  197,  204,  207,  224. 

95.  Acropolis,  Athens,  Restoration  of  West  End  of  . .186 

From  White’s  44  Plutarch.”  Mentioned  on  pages  186,  190,  210,  211,  216, 

219,  252,  259. 


ILL  US  TRA  LIONS, 


XXXI 


PAGE 

96.  Parthenon  at  Athens,  The 190 

From  Fergusson’s  “ History  of  Architecture. ” Mentioned  on  pages  15, 

186,  190,  201,  21 1.  See  index. 

97.  Ionic  Pillar  and  Entablature 204 

From  Cassell’s  44  Manual  of  Greek  Archaeology.”  Mentioned  on  pages 
203,  219,  220. 

98.  Corinthian  Capital  of  Pillar 220 

From  the  same.  Mentioned  on  pages  203,  220. 

99.  Pantheon  at  Rome,  The 223 

From  Cassell’s  41  The  World,  its  Cities  and  its  Peoples.”  Mentioned  on 
page  224. 

100.  St.  Paul’s,  Covent  Garden,  London 225 

From  Fergusson’s  “ History  of  Modern  Architecture.”  Mentioned  on 
page  224. 

101.  St.  Sophia,  Constantinople 226 

From  Lane-Poole’s  “Turkey.”  Mentioned  on  page  226. 

102.  Effect  of  Distance  on  Magnitude,  Light,  Contrast,  and 

Detail 235 

From  J.  W.  Stimson's  “Principles  and  Methods  in  Art  Education.” 
Mentioned  on  pages  13,  47,  234,  237,  241,  329,  369,  412. 

103.  Greek  Temple  Inscribed  in  Circles  Representing  Horizon 


Lines 236 

From  a drawing.  Mentioned  on  pages  234,  237,  239,  251,  255,  257,  258. 

104.  Optical  Illusions  Caused  by  Lines  Arranged  as  in 

Pediments 240 

From  the  Architectural  Record.  Reproduced  from  Thiersch’s  “ Op- 
tische  Tauschungen  auf  dem  Gebiete  der  Architectur.”  Mentioned  on 
pages  240,  241,  242,  250,  254,  256. 

105.  Optical  Illusions  with  Two  Parallel  Horizontal  Lines,  241 

From  the  same.  Mentioned  on  page  241. 


106.  Optical  Illusions  with  Three  Parallel  Horizontal 


Lines 242 

From  the  same.  Mentioned  on  pages  242,  243. 

107.  Maison  Carree,  Showing  Cornice  Curve  ....  245 

From  the  same,  drawn  by  J.  W.  McKechnie.  Mentioned  on  pages  246, 

249,  250,  251,  252,  255,  258. 

108.  Photographic  Effect  of  the  Same  Cornice  . . . 247 


From  the  same,  drawn  by  the  same.  Mentioned  on  pages  239,  246,  249, 
25°,  251,  255,  258. 


XXX i i ILL  US TRA  TLOJVS. 

PAGE 

109.  Photographic  Effect  of  Curved  Stylobate  and  Column 

of  Parthenon 251 

From  the  same.  Mentioned  on  pages  250,  255,  258,  260. 

no.  Fingers,  One  Behind  the  Other,  as  Seen  with  Each 

Eye 269 

From  Le  Conte’s  “Sight.”  Mentioned  on  page  26q. 

111.  The  Same  Fingers  as  Seen  with  Both  Eyes  . . . 269 

From  the  same.  Mentioned  on  pages  269,  273,  279,  280. 

1 1 2.  Same  Object  as  Seen  Differently  by  Each  Eye  . . . 272 

From  Le  Conte’s  “ Sight.”  Mentioned  on  pages  271,  272,  274,  280. 

1 13.  Parts  of  Objects  as  Seen  with  Near  and  Distant  Back- 

grounds 272 

From  the  same.  Mentioned  on  pages  234,  268,  273,  280. 

114.  Lens  of  Eye  Adjusted  to  Near  and  Distant  Objects  . 273 

From  the  same.  Mentioned  on  pages  231,  273,  323. 

115.  Field  of  View  of  Both  Eyes 278 

From  Foster’s  “Text  Book  of  Anatomy.”  Mentioned  on  pages  276, 

277,  278,  279. 

116.  Field  of  Distinct  Vision  for  Both  Eyes  Together  . 278 

From  a drawing.  Mentioned  on  pages  277,  280,  288. 

1 17.  Egyptian  Vase  and  Doll 283 

From  Wilkinson's  “ Ancient  Egyptians.”  Mentioned  on  pages  284,  295. 

118.  Prize  Vases  for  Athenian  Games 283 

From  Liibke’s  “ History  of  Art.”  Mentioned  on  pages  284,  295. 

119.  Building  Enclosed  by  Circles 284 

From  a drawing.  Mentioned  on  page  284. 

120.  Vases,  Outlines  by  Ellipses  and  Segments  of  Circles  . 285 

Drawn  about  forms  suggested  in  Hay’s  “ Ornamental  Geometric  De- 
signs,” etc.  Mentioned  on  pages  68,  286,  287,  295. 

121.  Curved  Lines  as  Outlined  by  Ellipses  ....  287 

From  a drawing.  Mentioned  on  page  287. 

122.  Beasts,  Fishes,  and  Birds  as  Outlined  by  Ellipses  . 289 

From  D.  R.  Hay’s  reproduction  from  Jardine’s  “ Naturalist’s  Library.” 
Mentioned  on  pages  78,  288,  295. 

123.  Outlines  of  Curves  as  Determined  by  Changes  in  Back- 

grounds   293 

From  a drawing.  Mentioned  on  pages  292,  293,  294,  295. 


ILL  US  TR A TIONS. 


xxxiii 


PAGE 

124.  Breaking  up  a Ray  of  White  Light 310 

From  Cassell’s  “ Science  for  All.”  Mentioned  on  page  310. 

125.  Formation  of  Complementary  Colors  ....  330 

From  Von  Bezold’s  “ Theory  of  Color.”  Mentioned  on  page  331. 

126.  Formation  of  Complementary  Colors  ....  331 

From  the  same.  Mentioned  on  page  331. 

127.  Color  Chart 334 


From  the  same.  Mentioned  on  pages  333-336.  390-393,  398,  403,  414. 

128.  Cones  and  Rods  in  Different  Parts  of  the  Retina  . 350 

From  Le  Conte’s  “Sight.”  Mentioned  on  pages  349,  350,  381. 

129.  The  Descent  from  the  Cross  : Rubens  ....  359 

From  a photograph.  Mentioned  on  pages  59,  303,  358,  363,  365,  367,  369. 

130.  Section  of  Retina 380 

From  Le  Conte’s  “ Sight.”  Mentioned  on  pages  349,  380,  383. 

131.  Generalized  Section  of  Retina  Showing  Inner  and 

Outer  Rods  and  Cones 381 

From  Foster’s  “ Text-Book  of  Anatomy.”  Mentioned  on  pages  349, 

381,  383- 


The  author  wishes  to  express  his  sense  of  obligation  to  the  various  artists, 
publishers,  and  authors  to  whom  he  is  indebted  for  kind  permission  to  insert 
in  this  book  such  illustrations  as  are  owned  by  them,  or  are  protected  by 
their  copyrights,  especially  to  The  Architectiiral  Record , and  to  Messrs.  D. 
Appleton  & Co.,  Dodd,  Mead  & Co.,  Charles  Scribner’s  Sons,  Fowler  & 
Wells,  and  the  F.  A.  Stokes  Co.  of  New  York,  Cassell  & Co.  and  John  Mur- 
ray of  London,  and  Ebner  & Seubert  of  Stuttgart. 


PROPORTION  AND  HARMONY  OF  LINE 
AND  COLOR  IN  PAINTING,  SCULP- 
TURE, AND  ARCHITECTURE. 


CHAPTER  I. 

CORRESPONDENCES  BETWEEN  THE  ELEMENTS  OF  FORM 
IN  THE  ARTS  OF  SOUND  AND  OF  SIGHT. 

Object  ol  the  Present  Volume — Connection  between  the  Subjects  Treated  in 
it  and  the  Requirements  of  Beauty — Similarity  of  these  Requirements 
in  the  Arts  of  Sound  and  of  Sight — Chart  of  the  Methods  of  Art- 
Composition — Sounds  are  Perceived  in  Time,  Sights  in  Space — Sounds 
are  Separated  by  Silences  or  Pauses,  Sights  by  Lines  or  Outlines — 
Sounds  may  Differ  in  Duration,  Force,  Quality,  and  Pitch  ; Sights  in 
Extension,  Light  and  Shade,  and  in  Quality  and  Pitch  of  Color — 
Respective  Correspondences  between  Effects  in  Sound  and  in  Sight — 
Combined  Influences  of  these  Effects  as  Manifested  in  Rhythm  and 
also  in  Proportion,  as  well  as  in  Harmony,  whether  of  Sound  or  of 
Sight. 

HT HE  mental  and  material  origin  of  the  methods  of  art- 
composition,  the  manner  and  order  of  their  develop- 
ment, and  the  correspondences  between  their  effects  as 
manifested  in  the  very  different  elements  entering  into 
form  in  the  different  arts,  were  unfolded  in  the  volume  of 
this  series  of  essays  entitled  “The  Genesis  of  Art-Form.” 
A summary  of  the  results  attained  in  that  volume  is 
printed  on  page  3 of  this  one  ; and  from  time  to  time 
references  will  be  made  to  them,  sufficiently  explicit,  it 


2 


PROPORTION  AND  HARMONY. 


is  hoped,  not  only  to  recall  to  those  who  have  read  the 
previous  discussion,  but  to  interpret  to  those  who  have 
not,  the  connection  between  the  line  of  thought  pursued 
then,  and  to  be  pursued  now.  This  connection  is  that 
between  the  more  generic  and  the  more  specific.  We  need 
to  know  not  merely  how,  in  all  the  different  arts,  the 
methods  of  composition  correspond,  but  also  how,  in  each 
art  and  each  product  of  it,  the  different  methods  operate 
conjointly. 

This  latter  is  a subject  which,  at  first  thought,  the  reader 
may  be  inclined  to  underrate,  supposing  it  to  be  subor- 
dinate, in  some  way,  to  certain  other  aesthetic  considera- 
tions. But  in  Chapter  XIV.  of  the  opening  volume  of  this 
series,  “ Art  in  Theory,”  it  was  shown  that  the  methods 
to  be  discussed  here  can  never  be  wisely  slighted,  because 
material  to  effects  not  merely  of  art-composition  but  also 
of  all  beauty,  whether  perceived  in  art  or  in  nature.  Ac- 
cordingly this  book,  in  the  degree  in  which  it  attains  its 
end,  will  reveal  not  only  the  requirements  of  proportion 
and  harmony  in  line  and  color,  but  also,  at  the  same  time, 
as  a consequence  of  its  general  subject,  the  requirements 
of  any  visible  art-form  when  so  composed  as  to  produce 
an  effect  of  beauty. 

The  volume  entitled  “ Rhythm  and  Harmony  in  Poetry 
and  Music  ” was  written  to  apply  the  principles  to  be 
unfolded  in  this  book  to  audible  products  ; and,  as  one 
object  of  these  essays  has  been  to  indicate  the  corre- 
spondences between  the  arts,  the  first  chapter  of  that 
work  was  devoted  to  indicating  how  the  factors  entering 
into  rhythm  may  be  correlated  to  those  entering  into 
proportion  ; as  well  as  how  the  factors  entering  into  har- 
mony of  tone  may  be  correlated  to  those  entering  into 
harmony  of  line  or  color.  For  the  benefit  of  readers  who 


METHODS  OF  ART-COMPOSITION. 


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Mind  and  CONSONANCE.  DISSONANCE.  INTERCHANGE.  ) 

Matter.  V PROGRESS. 

“ Gradation.  Abruptness.  Iransition.  i 


4 


PROPORTION  AND  HARMONY. 


have  not  had  access  to  that  volume,  a brief  recapitulation 
of  what  was  said  there  will  not  be  out  of  place  here. 

The  first  fact  that  was  noticed  there  was  that  poetry 
and  music  are  composed  of  elements  of  sound  appealing 
to  the  ear  in  the  order  of  time,  and  that  painting,  sculp- 
ture, and  architecture  are  composed  of  elements  of  sight 
appealing  to  the  eye  in  the  order  of  space. 

A second  fact  noticed  was  that,  as  a condition  for  con- 
structing a form  whether  appealing  to  the  ear  or  eye,  one 
must  be  able  to  apprehend  and  use  more  than  one  sound 
or  one  object  of  sight.  A sound  single  in  the  sense  of 
manifesting  neither  alteration  nor  cessation,  would  soon 
come  to  convey  no  more  intelligence  to  the  ear  than  ab- 
sence of  sound  ; and  a single  hue  of  the  same  shade  from 
nadir  to  zenith  would  soon  convey  no  more  intelligence 
to  the  eye  than  absence  of  hue.  In  order  to  be  understood 
and  used  by  a man  who  cannot  conceive  of  time  or  space 
except  as  it  is  divided  into  parts,  that  which  is  heard  must 
be  interrupted  by  periods  of  silence  and  that  which  is 
seen  must  be  separated  from  other  things  by  outlines. 
This  is  the  same  as  to  say — and  here  we  may  refer  to  the 
chart  on  page  3 — that  what  we  hear  must  have  a certain 
limit  of  duration  indicated  by  pauses  in  the  sound  ; and 
that  what  we  see  must  have  a certain  limit  of  extension  in- 
dicated by  lines.  How  shall  the  artist  determine  what 
these  limits  shall  be?  Fortunately,  in  the  more  important 
regards,  nature  herself  has  determined  them.  As  for 
poetry  and  music,  they  are  both  developed  primarily 
from  methods  of  using  the  human  voice,- — in  the  one  case 
in  speech,  in  the  other  in  song;  and,  secondarily,  from 
methods  in  Avhich  sounds  external  to  man  are  produced. 
But  whenever  the  human  voice  is  used,  pauses  are  used, 
both  at  comparatively  short  intervals,  after  separate  words 


CORRESPONDENCES  BETWEEN  SOUNDS  AND  SIGHTS.  5 

and  notes,  and  also  at  longer  intervals  where  it  is  neces- 
sary for  the  lungs  to  draw  in  air;  and  whenever  sounds 
that  are  not  produced  by  the  human  voice  are  heard,  they 
too  are  separated  by  intervals  of  silence.  Painting,  sculp- 
ture, and  architecture,  again,  are  developed  from  the 
methods  in  which  men  use  or  perceive  objects  in  the  ex- 
ternal world.  All  of  these  reveal  outlines  not  only  separat- 
ing them  from  other  objects,  but  generally  also  separating 
their  own  constituent  parts  from  one  another.  What 
more  natural  than  that  the  artist  should  accept  such 
arrangements  of  everything  heard  or  seen  in  nature,  and 
should  let  them  determine,  according  to  methods  of  imi- 
tation, the  relative  duration  or  extension  that  shall  be 
manifested  in  his  works?  As  a fact,  we  know  that  this  is 
exactly  what  he  does  do. 

Duration  and  extension,  however,  are  not  the  only  con- 
ditions that  the  artist  must  consider.  As  shown  in 
“ Poetry  as  a Representative  Art,”  Chapter  III.,  sounds 
may  differ  not  merely  in  duration  or  the  quantity  of  time 
that  they  fill  ; but  in  force,  or  the  stress  with  which  they 
are  produced,  making  them  loud  or  soft,  abrupt  or  smooth, 
etc. ; also  in  quality,  making  them  sharp  or  round,  full 
or  thin,  aspirate  or  pure,  etc.  ; and  in  pitch,  making  them 
high  or  low,  or  rising  or  falling  in  the  musical  scale.  Sights, 
too,  may  differ  in  analogous  ways ; i.  e.,  not  merely  in 
extension  or  the  quantity  of  space  that  they  fill,  which 
is  the  same  thing  as  size;  but  in  contour,  which  is  the 
same  thing  as  shape,  and  is  shown  by  the  appearance  of 
forcible  or  weak  lines  of  light  and  shade  ; also  in  quality  of 
color,  which  has  to  do  with  their  tints  and  shades  and 
mixtures  ; and  in  pitch  of  color,  which  is  determined  by 
the  hue. 

In  addition  to  merely  stating  these  facts,  it  may  be 


6 


PROPORTION  AND  HARMONY. 


well  to  enlarge  upon  one  or  two  of  them.  Notice,  for  in- 
stance, how  true  it  is  that  force  which  gives  emphasis  to 
sounds,  rendering  them  more  distinct  from  one  another 
than  would  be  the  case  without  it,  corresponds  to  light 
and  shade , which  emphasize  and  render  more  distinct  the 
contour  through  which  one  portion  of  space  having  a 
certain  shape  is  clearly  separated  from  another.  Notice, 
also,  that  accented  and  unaccented  syllables  or  notes,  as 
they  alternate  in  time,  perform  exactly  analogous  func- 
tions to  those  of  light  and  shade,  as  they  alternate  in 
space.  The  impression  of  form,  for  instance,  which,  so  far 
as  it  results  from  metre,  is  conveyed  by  varying  force  and 
lack  of  force  in  connection  with  divisions  made  in  time,  is 
the  exact  equivalent  of  that  impression  of  form  which,  so 
far  as  this  results  from  shape,  is  conveyed  by  varying 
light  and  shade  in  connection  with  divisions  made  in 
space.  Notice,  again,  that  quality  and  pitch  are  terms 
almost  as  much  used  in  painting  as  in  music,  quality  in 
colors  depending,  in  a way  analogous  to  quality  in  sounds, 
on  the  mixture  of  hues  entering  into  the  general  effect ; 
and  pitch  in  colors  depending  on  the  subdivision  of  light 
to  which  each  color  is  due.  Undoubtedly,  too,  it  is  owing 
partly  to  a subtle  recognition  of  the  correspondences  just 
indicated  that  to  certain  effects  in  the  arts  both  of  sound 
and  of  sight  the  more  general  terms,  tone  and  color , have 
come  to  be  applied  interchangeably. 

Later  on,  in  connection  with  the  various  divisions  and 
subdivisions  under  which  will  be  treated  the  different 
phases  of  form  to  be  considered,  it  will  be  shown  in  what 
way  each  phase  is  influenced  by  the  different  methods 
which,  on  page  3,  are  represented  as  instrumental  in  its  de- 
velopment. Here  it  is  sufficient  to  say  that  duration , lim- 
ited by  pauses  in  connection  with  force,  as  applied  to  the 


CORRESPONDENCES  BETWEEN  SOUNDS  AND  SIGHTS.  7 

accents  of  syllables  or  notes,  gives  rise  to  rhythm;  that 
extension , limited  by  outlines  in  connection  with  light  and 
shade,  as  applied  to  contour  or  shape,  gives  rise  to  propor- 
tion ; that  quality  and  pitch  of  tone  taken  together  fur- 
nish the  possibility  of  developing  the  laws  of  the  harmony 
of  sound ; and  that  quality  and  pitch  of  color  furnish 
the  same  possibility  with  reference  to  the  laws  of  the 
harmony  of  color.  It  is  important  to  notice,  too,  that 
force  or  accent,  while  having  to  do  mainly  with  rhythm, 
has  a certain  influence  also  upon  tone — in  poetry  upon 
the  tunes  of  verse,  and  in  music  upon  the  melodic  sug- 
gestions of  different  degrees  of  animation  ; also  that,  in  the 
same  way,  light  and  shade,  while  having  to  do  mainly  with 
outline  and  proportion,  have  a certain  influence  also  upon 
color.  They  change  it  in  order  to  interpret  the  meaning 
which  a colored  surface  is  intended  to  convey,  as,  for  in- 
stance, whether  it  is  to  represent  what  is  flat  or  round. 
They  suggest,  too,  the  vitality  characterizing  nature.  Cor- 
respondingly, also,  it  is  important  to  notice  that  quality 
and  pitch  of  sound  are  often  necessary  for  the  full  effects 
of  force  as  applied  to  rhythm ; and  that  the  same  ele- 
ments of  color  are  often  necessary  for  the  full  effects  of 
light  and  shade  as  applied  to  proportion.  In  fact,  when 
used  in  the  same  art,  the  different  special  effects  that  enter 
into  the  general  effects  of  proportion  and  harmony  which 
are  now  to  be  considered  are  none  of  them  produced  ex- 
clusively according  to  one  method  or  to  one  combination 
of  methods,  but  more  or  less  according  to  all  of  them  when 
operating  conjointly. 


1 


CHAPTER  II. 


MEANING  OF  PROPORTION  AND  THE  RECOGNITION  OF  IT 
IN  ART  AND  NATURE. 

Proportion  as  Meaning  Measurement,  and  a Comparison  of  Measurements, 
either  Absolute  or  Relative — As  Indicating  Relationships  or  Ratios  of 
Measurement,  or  Likeness  or  Equality  of  these — Tendency  of  the  Mind 
to  Make  Relative  Measurements  of  Spaces  Illustrated — Historical 
Evidences  of  the  Existence  of  this  Tendency — Primitive  Ornamenta- 
tion— Later  Ornamentation — Additional  Examples — The  Same  Tend- 
ency as  Manifested  in  Reproductions  of  Objects  Imitated — Proportion 
as  Manifested  in  Nature  as  a Whole  and  in  its  Parts — The  Subject  Im- 
portant and  Complex — Its  Analogy  to  Rhythm — Ratios  Used  in  Poetry 
and  Music — In  the  Longer  Rhythmic  Divisions  of  Both  Arts— Rhythmic 
Ratios  are  Represented  by  Small  Numbers,  and  thus  Rendered  easily 
Recognizable — Same  Principle  Applicable  to  Proportion — Proportion 
may  be  Recognized  without  a Recognition  of  the  Exact  Ratio  Causing 
it — The  Use  by  the  Greeks  of  Ratios  Represented  by  Small  Numbers. 

T'HE  term  proportion,  when  used  in  a non-technical 
sense,  signifies  frequently  little  more  than  measure- 
ment. When  we  say  that  a house  has  the  proportions  of 
a palace,  or  a growing  boy  the  proportions  of  a man,  we 
mean  merely  that  the  one  is  as  large  as  the  other,  or  has 
the  same  general  measurements.  In  addition  to  this, 
however,  there  is  often  connected  with  the  term,  when 
carefully  used,  a conception  of  a comparison  of  measure- 
ments. When  we  say  of  a man  that  his  feet  are  out  of 
proportion,  or  of  a copy  of  a Greek  temple,  that  its  pedi- 
ment is  out  of  proportion,  we  are  probably  recalling  a 
normally  developed  man  or  an  ancient  Greek  temple.  If 

8 


MEANING  OF  PROPORTION. 


9 


so,  we  mean  that,  in  the  specimen  before  us,  the  meas- 
urements of  the  parts  mentioned  are  not  the  same  as  in 
the  specimen  of  which  we  are  thinking. 

There  may  be  two  reasons  why  these  measurements  are 
not  the  same:  one  reason,  because  they  are  absolutely 
larger  or  smaller  than  in  this  specimen  ; the  other  reason, 
because  they  are  relatively  so,  a hand  or  a limb  being  said 
to  be  in  proportion  because  its  measurements,  whether 
large  or  small,  bear  the  same  relation  to  the  parts  or  to 
the  whole  of  a body  that  they  do  in  the  typical  man 
which  is  supposed  to  be  the  artist’s  model. 

But  proportion  has  still  another  meaning.  From  this, 
any  conception  of  imitation,  whether  or  not  suggested  by 
any  particular  model,  is  absent  ; and  a part  is  said  to  be  in 
proportion  because  of  the  relationship  which  its  measure- 
ments sustain  to  the  measurements  of  other  parts  or  to 
the  whole  of  a product.  This  seems  to  be  the  meaning 
when  we  speak  of  the  proportions  of  the  human  figure, 
irrespective  of  any  references  to  attempts  to  copy  any  par- 
ticular model;  and  it  certainly  is  the  meaning  when  we 
speak  of  the  proportions  of  a building  in  a style  such 
as  has  never  before  had  existence.  Evidently,  too,  this 
latter  use  of  the  term  is  the  one  which  we  need  chiefly  to 
consider  in  this  volume,  our  main  object  being  not  to 
show  how  certain  standards  of  proportion  can  be  imitated, 
but  what  there  is  in  them  that  makes  them  worthy  of 
imitation  ; and  in  what  way,  in  the  case  of  architecture  at 
least,  new  forms,  by  being  constructed  according  to  the 
principles  exemplified  in  the  old,  may  be  made  to  manifest 
the  old  characteristics.  Notice  also  that,  in  this  sense, 
proportion  includes  the  ideas,  both  of  ratios  or  relation- 
ships, as  in  i : 2,  and  also  of  likeness  or  equality  in  ratios, 
as  in  i : 2 : : 3 : 6. 


10 


PROPORTION  AND- HARMONY. 


Observe,  too,  the  connection  between  what  has  just 
been  said  and  what  was  said  in  the  last  chapter,  viz.,  that 
proportion  is  to  effects  in  sight  what  rhythm  is  to  effects 
in  sound.  Just  as,  in  rhythm,  pauses  separate  syllables 
or  notes,  and,  aided  by  the  absence  or  presence  of  force 
in  the  accents,  divide  the  whole  duration  of  a series  of 
sounds  into  like  parts  or  multiples  of  parts  ; so,  in  pro- 
portion, it  is  possible  for  lines  to  separate  objects  of  sight, 
and,  aided  by  light  and  shade  revealing  their  shapes,  to 
divide  the  whole  extent  of  space  covered  by  a series  of 
forms  into  like  parts  or  multiples  of  parts,  all  of  which 
may  be  shown  thus  to  have  measurements  exactly  related 
to  one  another  or  to  the  whole. 

But  if  it  be  possible  to  divide  spaces  thus,  is  it  probable 
that  any  or  many  will  care  to  do  this  ? The  moment  that 
the  question  is  asked,  it  will  be  found  to  admit  of  but 
one  answer.  Such  a method  of  measuring  spaces  is  not 
only  probable  but  inevitable.  Apparently  the  mind,  in 
arranging  different  objects  of  sight,  or  in  judging  of  their 
effects  as  it  finds  them  arranged,  cannot  avoid  making 
these  measurements.  None  of  us  can  look  at  window- 
panes,  doors,  or  facades  of  buildings,  without  comparing 
the  lengths  and  breadths  of  each.  It  is  true  that  we  do 
not  always  compare  them  consciously.  But  if  one  dimen- 
sion be  greater  than  another,  we  usually  perceive  the  fact, 
and  form  an  estimate  as  to  how  much  greater  it  is.  After 
a most  limited  glance  at  a building,  we  describe  it  to 
others  by  saying  that  it  is  two  or  three  times,  as  the 
case  may  be,  longer  than  it  is  high.  Or,  to  notice  the 
tendency  when  exemplified  in  action,  between  which  and 
the  mental  processes  necessitated  in  art  the  correspond- 
ence is  more  complete,  suppose  that  one  be  framing  an 
engraving  occupying  the  centre  of  a sheet,  about  which 


TENDENCY  TO  MEASURE  SPACES. 


II 


centre  there  must  be  a margin  on  all  sides.  Even  if  he 
have  never  seen  a picture  framed  before,  forty-nine  times 
out  of  fifty  he  will  place  the  engraving  so  that,  intervening 
between  it  and  the  frame,  there  shall  seem  to  be,  to  his 
eyes,  an  equal  amount  of  space  on  every  side  of  it,  or,  at 
least,  on  opposite  sides  of  it.  Or,  if  the  picture  must  be 
hung  on  a wall  between  two  doors,  he  will  hang  it  so  that, 
to  his  eyes,  there  shall  seem  to  be  an  equal  distance  be- 
tween the  frame  and  each  door.  Even  children,  if  build- 
ing houses  of  blocks,  will  select  blocks  of  similar  sizes  to 
be  put  in  corresponding  places  at  different  sides  of  the 
same  windows  and  porches. 

An  analogous  fact  is  true  universally,  and  always  has 
been  true.  There  is  no  primitive  kind  of  ornamentation, 
no  matter  how  barbarous  the  race  originating  it,  of  which 
one  characteristic,  perhaps  the  most  marked,  is  not  an 
exact  division  or  subdivision  of  spaces,  the  mind,  appar- 
ently, deriving  the  same  sort  of  satisfaction  from  rude 
lines  of  paint  and  scratchings  upon  stone,  made  at  pro- 
portional distances  from  one  another,  that  it  does  from  the 
rhythmical  sounds  (see  Fig.  A)  drummed  with  feet,  hands, 


3 3 3 3 6 


I 1 1 

, i 

=9=m=?=3= 

* S-m-m- 

nA 

or  sticks  to  accompany  the  song  and  dance  of  the  savage. 
In  fact,  an  arrangement,  as  in  the  staves  and  bars  that 
follow,  might  be  used  as  preparatory  either  for  writing 
music  or  for  decorating  with  color — i.  e.,  for  the  purpose  of 
representing  either  rhythm  or  proportion.  (See  Fig.  B.) 


12 


PROPORTION  AND  HARMONY. 


The  same  tendency  is  illustrated  in  the  two  following 
figures  (Figs.  I and  2).  They  are  very  ancient  forms  of 


FIG.  1. — VITRUVIAN  SCROLL. 
See  pages  12,  40. 


| Iff  ii 

EFj 

uiri  mm\ 

Hq 

m 

min  »■  lii-  iih 

a 

in  1 fiiiiii  _ 1 Inin  if 

M1G-H 

lil'i-lU 

FIG.  2. — GREEK  FRET. 

See  pages  12,  40. 

decoration  used  in  pottery,  goldsmith’s  work,  and  archi- 
tecture, but,  for  the  reason,  apparently,  that  they  are  per- 
fectly conformed  to  the  requirements  of  the  mind,  they 
are  used  to-day  almost  as  extensively  as  ever.  Notice  the 
same  tendency,  too,  in  the  triglyphs  and  metopes  which 
adorned  the  frieze  of  the  Greek  Doric  temple  (Fig.  3)  ; 
also  in  various  parts,  which  need  not  be  pointed  out,  in 
the  forms  in  Figs.  6 to  12,  on  pages  33  to  38. 


‘ Bsjmsg  tr'vaflmiwH  I )i'w  Eg  j gees 

FIG.  3.- TRIGLYPHS  AND  METOPES. 

See  pages  12,  40,  168. 


These  figures  indicate  that  equal  divisions  of  spaces 
satisfy  mental  demands  of  which  all  men,  whether  young 
or  old,  cultivated  or  uncultivated,  are  conscious.  It  is 
not  only  because  it  is  convenient,  but  because  it  is  artisti- 


PROPORTION  IN  NATURE. 


13 


cally  satisfactory,  that  in  all  sorts  of  decorative  work, 
whether  upon  stone,  wood,  paper,  or  cloth, — from  the 
finishing  upon  the  ridge-pole  of  a roof  to  the  lace  and 
fringe  upon  a window-curtain,  and  the  patterns  upon 
carpets  and  wall-papers, — outlines,  sometimes  subdivided 
with  great  variety,  but  nevertheless  covering  like  spaces, 
are  put  together. 

Nor  is  this  tendency  exhibited  in  merely  those  depart- 
ments of  art  in  which  the  mind  works  upon  forms  origi- 
nated almost  wholly  by  itself.  It  is  found  also  in  forms 
which,  with  more  or  less  literalness,  are  copied  from  nature. 
Just  as  poetry  can  take  words  and  phrases,  actually  heard 
in  conversation,  and  rearrange  them  in  such  ways  as  to 
fulfil  the  requirements  of  rhythm,  so  painting  and  sculp- 
ture can  take  outlines  perceived  in  nature,  and  rearrange 
them  in  such  ways  as  to  fulfil  the  requirements  of  pro- 
portion. 

Of  course,  this  could  not  be  the  case  unless,  to  some 
extent,  the  requirements  of  proportion  were  fulfilled  in 
nature.  In  Chapter  II.  of  “ Rhythm  and  Harmony  in 
Poetry  and  Music  ” it  was  shown  that  rhythm  is  a charac- 
teristic of  natural  forms.  Notice  now  that  the  same  is 
true  of  proportion.  Take  nature  as  a whole.  The  sky 
and  earth  always  divide  the  possible  field  of  vision, 
approximately  at  least,  into  two  equal  and  complement- 
ary parts.  When  the  painter  composing  his  picture  ac- 
cording to  the  laws  of  perspective  (see  Chapter  XIV., 
page  233,  and  Fig.  102,  page  235)  decides  upon  the  places 
for  his  horizon,  his  vanishing  point,  and  his  principal  fig- 
ures, and  upon  the  distances  of  these  from  one  another, 
and  from  the  margins  on  either  side  of  his  composition, 
as  well  as  upon  the  sizes  and  shapes  of  his  trees,  houses, 
men,  animals,  considered  in  themselves  or  in  connection 


14 


PROPORTION  AND  HARMONY. 


with  other  objects  near  them  or  remote  from  them,  he 
makes  his  decisions  as  a result  of  relative  measurements, 
mental  or  actual.  And  so  with  reference  to  the  different 
members  and  the  general  shape  of  the  human  form,  or  of 
the  forms  of  animals,  trees,  plants,  or  of  any  objects,  in 
fact,  that  are  transferred  from  nature  to  canvas  or  marble 
by  way  of  imitation, — it  is  as  a result  of  a certain  compari- 
son of  measurements  between  part  and  part,  that  one  can 
say  that  certain  of  these  forms  are  or  are  not  in  propor- 
tion. Take,  for  instance,  a very  heavy  body,  either  of 
flesh  or  of  foliage,  supported  by  very  slight  limbs  ; should 
we  not  say  at  once  that  the  parts  were  out  of  proportion  ? 
Or  take  the  case  of  limbs  jointed,  as  at  the  elbow  or  knee, 
and  one  of  them  very  much  longer  than  the  other  ; should 
we  not  say  at  once  that  the  two  were  out  of  proportion? 
Even  of  such  small  details  as  eyes,  ears,  hands,  and  nos- 
trils we  should  make  a similar  affirmation,  in  case  discrep- 
ancies in  measurements  were  apparent.  And  though  the 
relative  sizes  of  parts  differ  greatly  in  individual  instances, 
they  are  always  in  the  same  body  expected  to  be  so  re- 
lated, each  to  each,  and  to  other  members,  as  to  show  an 
effect  that  can  be  recognized  only  as  a result  of  comparing 
measurements. 

At  first  thought,  the  action  of  the  mind  in  making  these 
comparisons  may  seem  to  be  of  little  importance,  scarcely 
worthy  of  the  serious  attention  which  evidently  we  are 
about  to  give  it.  But,  in  this  life,  it  usually  takes  very 
little  to  start  that  which  may  develop  into  very  much. 
Rhythm,  too,  is  apparently  of  little  importance.  If  one 
knew  nothing  about  art,  what  could  appear  more  absurd 
than  for  an  intelligent  man  to  think  it  worth  while,  when 
wishing  to  say  something,  to  count  the  syllables  that  he 
utters,  so  that  they  shall  reveal  exact  divisions  and  sub- 


PR  OP  OR  TION  IMP  ORTA  NT. 


15 


divisions  of  time,  such  as  the  negro  makes  when  he  beats 
his  hands  and  feet  for  dancers?  Yet  it  is  out  of  this 
simple  method  of  counting,  that  art  has  developed  the 
most  important  element  in  the  form  of  poetry,  as  well  as  an 
element  extremely  important  in  the  form  of  music.  When 
we  come  to  examine  the  different  combinations  of  effects 
attributable  to  rhythm,  we  find  that  we  are  by  no  means 
dealing  with  a subject  so  simple  as  at  first  appeared.  The 
same  is  true  of  proportion.  Before  deciding,  for  instance, 
that  a foot  or  a nose  is  disproportionately  large  or  small, 
it  must  be  compared  not  only  with  other  feet  and  noses, 
but  with  the  sizes  of  all  the  other  surrounding  features  in 
the  animal  or  man  in  which  it  appears.  The  same  feature 
may  look  too  large  with  small  surroundings,  and  too  small 
with  large  ones.  Indeed,  the  number  and  variety  of 
measurements  that  any  extensive  knowledge  or  applica- 
tion of  proportion  involves  are  almost  incalculable.  When 
we  try  to  determine  exactly  what  it  is  that  causes  its  re- 
sults to  be  satisfactory,  in  the  human  form,  for  instance 
(see  Figs.  31,  page  57  ; 32,  page  58;35>Page  7°  I 36- Page 
71  ; 45,  page  86  ; 62,  page  121  ; 63,  page  122  ; 69,  page  128  ; 
73,  page  137;  and  74,  page  139),  or  in  buildings  like  the 
Parthenon  (see  Fig.  96,  page  190;  also  pages  21 1 to  214), 
or  the  Grand  Opera  House  at  Paris  (see  Fig  86,  page  167 ; 
also  pages  170  and  1 7 1),  then  we  begin  to  perceive  that  this 
characteristic,  as  is  true  of  every  other  entering  into  the 
effects  of  beauty  (see  page  160  of  “ Art  in  Theory  ”),  is  capa- 
ble of  complexities  as  well  as  possibilities  almost  infinite. 

The  best  way  of  beginning  to  understand  the  complexi- 
ties of  any  method  of  expression  is  by  trying  to  understand 
its  elementary  processes.  Elementary  proportional  pro- 
cesses may  be  rendered  most  intelligible,  perhaps,  by  dwell- 
ing for  a little  upon  the  correspondences,  already  many 


1 6 


PROPORTION  AND  HARMONY. 


times  suggested,  between  proportion  and  rhythm.  In  the 
volume  entitled  “ Rhythm  and  Harmony  in  Poetry  and 
Music  ” rhythm  was  shown  to  result  from  the  mind’s  en- 
deavor, in  the  element  of  time  or  duration,  to  arrange  the 
features  of  form  in  such  a way  as  to  be  able  to  conceive  of 
them  as  a unity.  (See  the  note  beginning  on  page  61.)  It 
was  pointed  out  that  it  is  in  order  to  accomplish  this  end 
that  the  mind  divides  the  composition  as  a whole  into 
equal  or  approximately  equal  parts  determined  by  the 
duration  of  each  part.  These  parts  in  poetry,  as  we 
know,  are  feet,  measures,  lines,  verses,  couplets,  triplets, 
stanzas,  cantos,  etc.,  and  in  music  are  measures,  motives, 
phrases,  sections,  periods,  etc.  Now  notice  that  in  poetry, 
in  the  smallest  of  these  divisions, — feet,  or  measures  as  they 
are  also  called, — -there  are  never  more  than  one,  two,  three, 
four,  or,  at  most,  five  syllables.  That  is  to  say,  as  measured 
by  the  syllables,  the  successive  feet,  so  far  as  concerns  their 
duration,  are  to  one  another  as  I to  I,  I to  2,  I to  3,  1 to  4, 
1 to  5,  2 to  3 (2  to  4,  which  is  the  same  as  r to  2),  or  as  3 
to  4.  As  may  be  seen  by  referring  to  pages  1 1 to  1 3 and  26 
to  37  of  “ Rhythm  and  Idarmony  in  Poetry  and  Music,” 
these  ratios  represent  all  that  are  used  in  poetic  measures. 
In  music  the  measures  are  filled  with  a certain  fixed  num- 
ber of  notes,  or  rests  corresponding  to  them.  Of  these, 
the  longest  note  ordinarily  used  is  the  whole  note,  to 
which,  as  a rule,  is  given  the  same  duration  as  to  two  half 
notes,  four  quarter  notes,  eight  eighth  notes,  sixteen  six- 
teenth notes,  and  thirty-two  thirty-second  notes,  e.  g.: 


m 


i-i- 


+ * + + 


(c) 


All  these  notes,  however,  whether  we  express  their 
ratios  by  the  numbers  I to  2,  1 to  4,  etc.,  or  by  2 to  4,  2 


PROPORTION  AND  RHYTHM , 


17 


to  8,  etc.,  represent  comparatively  little  variety.  Each  is 
simply  the  ratio  1 to  1 with  one  or  both  of  its  factors 
multiplied  by  a small  even  number.  Occasionally  also 
three  notes,  like  those  in  the  measures  marked  3 in  the 
music  on  page  1 1,  can  be  given  the  same  time  as  would 
ordinarily  be  given  to  two  notes  of  the  same  length  as 
themselves,  or  to  one  note  twice  as  long.  In  the  same 
way  six  notes,  like  those  marked  6 in  the  same  music,  and, 
now  and  then,  five  notes,  marked  5,  can  be  given  the  same 
time  as  four  notes  of  the  same  length  as  themselves,  or 
two  notes  twice  as  long.  It  is  possible,  therefore,  through 
the  combined  effects  of  measures  and  notes  used  in  order 
to  produce  musical  rhythm,  to  have  represented  the  follow- 
ing ratios,  or  the  same  with  one  of  their  factors  multiplied 
by  a small  even  number,  viz.  : 1:1,  1 : 2,  1 : 3,  1 : 4,  1 : 5, 
1:6,  2:3,  2:5,  3:4,  3:5,  4:5,  and  5:6.  From  these 
ratios,  2 : 4,  2 : 6,  3 : 6,  and  4 : 6 are  omitted  because  they 
are  already  expressed  in  the  ratios  1:2,  1:3,  and  2 : 3. 

WILMOT. 


~*DSr^~ 

Life  and  joy  thy  beams  im  - part, 

-I- 


Ev  - ery  poor,  be  - night-ed  heart. 


-f= — 


(D) 


Still  less  variety  characterizes  the  ratios  representing 
the  relations,  each  to  each,  of  the  larger  divisions  made 
in  these  two  arts.  In  the  majority  of  cases,  successive 
poetic  lines,  couplets,  and  stanzas,  or  musical  motives, 


i8 


PROPORTION  AND  HARMONY. 


phrases,  sections,  and  periods  are  of  identical  length,  i.  e 
as  I : i.  Even  when  the  numbers  of  syllables  or  measures 
in  successive  lines  or  phrases  differ,  these  are  usually 
made  to  have  a similar  general  effect  by  a pause  in  poetry, 
or  a prolongation  in  music,  at  the  end  of  the  shorter  of  the 
lines,  thus  causing  all  to  seem  to  be  uttered  in  the  same 
time  (see  Fig.  D,  page  17.) 

The  longest  line  used  in  poetry  without  being  virtually 
a double  line,  and  one  as  long  as  any  usual  phrase  in 
music,  contains  eight  measures,  e.  g.  : 

“ Comrades,  leave  me  here  a little,  while  as  yet ’t  is  early  morn.” 

— Locksley  Hall : Tennyson. 

Were  this  to  be  alternated  with  a line  containing  seven 
measures  we  should  have  as  a ratio  representing  the  largest 
possible  numbers  in  poetic  rhythm  7:8,  but  in  reading 
such  lines  we  should  invariably  pause  after  the  shorter 
line  in  such  a way  as  to  cause  the  effects  of  the  two  lines 
together  to  appear  to  be  as  1 : 1.  Accordingly,  we  may 
say  that  the  effects  of  rhythm  are  produced  by  subdi- 
visions whose  relations  to  one  another  can  be  represented 
by  ratios  confined  to  small  numbers.  It  is  evident,  too, 
that  the  fact  that  they  are  small  is  that  which  enables  the 
mind  to  recognize  the  likeness  between  the  parts,  and  thus 
to  perceive  a unity  in  general  effect  notwithstanding  va- 
riety and  complexity  in  certain  details.  (See  page  3,  also 
the  note  beginning  on  page  61.)  Were  poetic  measures 
composed  of  from  five  to  seven  syllables,  or  poetic  lines 
of  from  eight  to  thirteen  measures,  we  should  very  often 
be  unable  to  recognize  either  the  character  of  the  metre 
or  its  existence. 

Evidently  the  same  principle  ought  to  be  illustrated  in 
proportion.  It  is  natural  to  suppose  that  just  as  the  mind, 
when  listening  through  the  ear,  takes  satisfaction  in  sounds 


RATIOS  OF  SMALL  NUMBERS. 


19 


so  divided  and  subdivided  as  to  duration  that  all  can  ap- 
pear to  be  parts  of  a unity,  because  all  can  be  measured 
according  to  some  clearly  recognized  standard  of  com- 
parison (see  note  on  page  61)  ; so  the  same  mind,  looking 
through  the  eye,  takes  satisfaction  in  objects  of  sight  so 
divided  and  subdivided  as  to  extension,  i.  e.,  as  to  size  or 
shape,  that  these  also  can  be  measured  and  compared. 
Notice,  too,  that  they  can  be  compared  with  ease  in  the 
degree  in  which  they  can  be  perceived  to  measure  exactly 
the  same,  i.  e.,  to  be  as  1 : 1 ; or,  if  not  so,  can  reveal  their 
relationships  to  1:1,  as  can  1 : 2 or  1:3,  because  it  means 
1 : 1 — (—  1 ; or  i : 1 — f-  1 — 1 . As  will  be  shown  hereafter, 
this  is  a condition  underlying  the  effects  of  proportion 
which  is  fundamental,  and  must  be  recognized  before  the 
subject  can  be  fully  understood. 

Notice,  again,  that  proportion,  as  it  is  thus  attributed  to 
measurements  that  are  compared,  is  merely  a statement  of 
a fact ; nor  is  it  essential  that  the  mind,  before  stating  this 
fact,  should  recognize  what  the  ratio  is,  only  that  it  has 
existence.  The  same  principle  applies  here  as  in  rhythm. 
To  experience  the  effects  of  this,  we  do  not  need  to  be 
able  to  tell  what  the  metre  is — whether  long  or  short, 
iambic  or  trochaic — only  that  there  is  a metre.  But  while 
this  is  true,  the  metre  must  be  capable  of  being  analyzed  ; 
and  we  must  feel  that  it  is  so,  although,  perhaps,  we  our- 
selves do  not  actually  go  through  with  the  analytic  process. 

What  has  been  said  will  show  us  a good  reason,  too, 
why,  as  affirmed  by  W.  W.  Lloyd  in  his  “ Memoir  on  the 
Systems  of  Proportion,”  published  with  Cockerill’s  “ Tem- 
ples of  Aigina  and  Bassaj,”  p.  64,  “ the  Greek  architects 
attached  great  value  to  simple  ratios  of  low  natural  num- 
bers.” Of  course,  the  simpler  the  ratio,  and  lower  the 
number,  the  more  easily  could  each  be  recognized. 


CHAPTER  III. 


EFFECTS  OF  PROPORTION  AS  WRONGLY  CONFOUNDED 
WITH  THOSE  OF  PERSPECTIVE. 

Difficulties  Experienced  in  Applying  Principles  of  Proportion — If  ever 
Understood  they  can  be  Understood  to-day — Necessity,  to  Rid  the  Sub- 
ject of  Complexity,  of  Separating  Two  Processes  in  Perception — First, 
the  Unconscious  Physical  Recognition  of  Appearances;  Second,  the 
Conscious  Mental  Measurement  of  them — As  Applied  to  Sounds,  the 
First  Process  Determines  Effects  of  Harmony  ; the  Second,  Effects  of 
Rhythm — So  in  Sights,  not  the  First,  but  the  Second,  Determines  Effects 
of  Proportion — -This  Results  from  the  Conscious  Measurement  of  Ap- 
pearances after  and  as  they  have  been  Perceived,  whereas  the  Uncon- 
scious Physical  Process  Determines  Effects  of  Perspective — The  T wo 
Processes  are  easily  Confounded,  with  Resulting  Difficulties  in  Theory 
and  Practice — -The  Two  Supposed  to  have  been  Confounded  by  the 
Greeks — This  Supposition  not  wholly  Tenable— Yet  at  the  Basis  of 
Modern  Theories  which  Correlate  Proportion  to  the  Effects  of  Musical 
Pitch  upon  the  Ear,  as  do  the  Theories  of  Legh  and  Zeising — Of  Hay, 
Fergusson,  Penrose,  and  Lloyd — Impossibility  of  any  Theoretic  or 
Practical  Understanding  of  Proportion  according  to  this  Conception 
of  it. 

T F,  as  shown  in  Chapter  Second,  the  principles  underly- 
^ ing  proportion  be  simple  in  character  as  well  as  simi- 
lar in  effect  to  those  of  rhythm,  it  would  seem  to  follow 
that,  like  those  of  rhythm,  they  should  be  comparatively 
easy  to  interpret  and  to  produce.  Why,  then,  are  they 
usually  treated  as  if  this  were  not  the  case  ? Why  are 
they  sometimes  attributed  to  laws  of  vision  with  which 
the  Greeks  alone  of  all  human  beings  have  been  ac- 
quainted, which  laws,  as  understood  by  them,  it  is  in  our 
day  next  to  impossible  to  discover  or  to  apply  ? 


20 


PROPORTION  AND  PERSPECTIVE. 


21 


In  endeavoring  to  answer  this  question,  let  us  begin  by 
recalling  the  fact  that,  if  a subject,  however  complex,  have 
once  been  made  to  appear  intelligible,  it  can  presumably 
be  made  to  appear  so  again.  It  need  not  be  supposed  to 
be  a mystery  wholly  impenetrable.  It  probably  can  be 
seen  through,  and  this  in  accordance  with  the  workings  of 
the  powers  of  observation  and  reflection  allotted  to  the 
ordinary  man  of  one’s  own  generation. 

Another  fact  that  it  is  well  to  recall  is,  that,  in  the  de- 
gree in  which  any  subject  appears  complex,  it  does  so 
because  the  elements  connected  with  it  have  not  been 
completely  analyzed.  How  is  it  with  those  connected 
with  proportion?  Let  us  see.  What  are  these  elements? 
— First  of  all,  a preliminary  effect  whereby  an  image  is  im- 
pressed on  the  retina.  Dr.  Henry  D.  Noyes,  in  his  “ Dis- 
eases of  the  Eye,”  gives  a picture  of  the  eye  of  a dead 
rabbit  in  which  are  seen,  photographed,  as  it  were,  parallel 
bars  that  had  been  held  in  front  of  the  eye  just  before  the 
animal  was  killed.  The  experiment  is  shown  in  proof  of 
the  theory  that  form  is  impressed  upon  the  visual  organs 
in  connection  with  the  chemical  action  of  the  fluids,  pro- 
ducing effects  analogous  to  those  produced  upon  the  nega- 
tive of  a photograph.  Aside  from  what  the  experiment 
indicates  with  reference  to  this  theory,  it  certainly  shows 
that  the  eye  has  in  it  a picture  of  the  form  as  a form.  In- 
deed, merely  by  looking  into  the  eyes  of  our  fellows,  we 
can  sometimes  see  in  them  an  image  of  the  external 
world  as  perfect  as  a reflection  in  a mirror.  “A  camera 
and  an  eye,”  says  Le  Conte  in  his  “Sight,”  “are  both 
contrived  for  the  same  purpose,  viz.,  the  formation  of  a 
perfect  image  on  a screen  properly  placed.  Look  into 
the  camera  from  behind,  and  we  see  the  inverted  image 
on  the  ground-glass  plate;  look  into  the  eye  from  behind, 


22 


PROPORTION  AND  HARMONY. 


and  we  see  also  an  inverted  image  on  the  retina.  [See 
Fig.  4.]  “The  camera  is  a small,  dark  chamber,  open 


FIQ.  4.  -ILLUSTRATION  OF  THE  FORMATION  OF  AN  IMAGE  ON  THE  RETINA. 

See  pages  22,  23,  234. 


to  the  light  only  in  front,  to  admit  the  light  from  the  ob- 
ject to  be  imaged.  It  is  coated  inside  with  lamp-black,  so 
that  any  light  from  the  object  to  be  imaged,  or  from  other 
objects,  which  may  fall  on  the  sides  will  be  quenched, 
and  not  allowed  to  rebound  by  reflection,  and  thus 

fall  on  the  image  and  spoil  it. 
So  the  eye  also  is  a very  small, 
dark  chamber,  open  to  light 
only  in  front,  where  the  light 
must  enter  from  the  object  to 
be  imaged,  and  lined  with  a dark 
pigment  to  quench  the  light  as 
soon  as  it  has  done  the  work  of 
impressing  its  own  point  of  the 
retina,  and  thus  prevent  reflec- 
tion and  striking  some  other 
part  and  thus  spoiling  the  image. 
Both  camera  and  eye  form 
their  images  by  means  of  a lens 
or  a system  of  lenses.”  (See 
Fig.  5,  above.)  The  way  in 
which  the  rays  of  light  pass  through  the  crystalline  lens 


FIG.  5.— THE  CAVITY  OF  THE 
EYE. 

a,  outer  layer  ; e , crystalline  lens  ; 
g , retina  ; /z,  optic  nerve. 

See  pages  21,  22. 


PROPORTION  AND  PERSPECTIVE. 


23 


of  the  eye  and  impress  upon  the  retina  an  inverted  but 
exact  image  of  the  thing  seen  is  illustrated  in  Fig.  4, 
page  22.  But  notice  now  that  the  production  of  this 
image  is  not  all  that  is  necessary  in  order  to  produce  the 
impression  of  proportion.  Besides  being  made  to  per- 
ceive the  image,  the  mind  must  perceive  the  relative 
measurements  of  different  parts  of  the  image. 

Manifestly  the  first  of  these  effects  involves  a very  dif- 
ferent process  from  the  second.  The  first  is  wholly  de- 
pendent upon  the  operation  of  physical  laws,  an  operation 
in  which  the  organs  of  sight  take  care  of  themselves, 
through  processes  of  which  the  mind  is  wholly  uncon- 
scious. The  second  of  the  effects  is  wholly  dependent 
upon  mental  action,  as  much  so  as  that  of  a man  deter- 
mining with  a tape-measure  the  relative  dimensions  of  an 
image  in  a mirror.  These  dimensions  cannot  be  recog- 
nized as  sustaining  certain  relations  to  one  another  except 
as  the  mind,  as  a result  of  comparison,  forms  judgments 
with  reference  to  them. 

In  Chapters  VII.  to  XV.  of  the  volume  entitled 
“ Rhythm  and  Harmony  in  Poetry  and  Music,”  it  was 
shown  that  effects  of  harmony,  as  developed  in  poetry  or 
in  the  scales  and  chords  of  music,  are  determined  by  the 
action  of  the  physical  organs  of  hearing,  irrespective  of  any 
conscious  action  of  the  mind  ; and  in  Chapters  II.  to  VI.  of 
the  same  book,  it  was  shown  that  effects  of  rhythm,  as  de- 
veloped in  either  art,  are  determined  by  the  conscious  ac- 
tion of  the  mind  when  comparing  the  measurements  of 
different  syllables,  notes,  feet,  or  phrases — that  is  to  say,  it 
was  shown  that,  before  recognizing  or  constructing  rhythm, 
the  physical  organs  of  hearing  report  to  the  mind  certain 
sounds;  and  afterwards  that  the  mind,  by  purely  psycho- 
logical and  conscious  processes,  measures  the  different 


24 


PROPORTION  AND  HARMONY. 


lengths  of  different  sounds,  or  the  different  degrees  of 
their  intensity,  and  thus  estimates  or  arranges  their 
rhythmic  possibilities. 

Now  with  these  facts  concerning  sounds  in  mind,  let  us 
consider  again  the  two  elements  underlying  the  perception 
of  external  objects.  Here,  also,  we  shall  find  physical  pro- 
cesses of  which  the  mind  is  unconscious,  as  a result  of  which 
an  image  of  different  shadings  or  colors  is  made  to  appear 
on  the  retina.  Is  it  not  clear  that  these  processes  corre- 
spond to  those  resulting  from  the  physical  actions  of  the  ear, 
which,  while  preparatory  to  rhythm,  do  not  themselves  pro- 
duce or  determine  it?  And,  if  so,  is  it  not  logical  to  infer 
that  these  processes  in  the  eye,  while  preparatory  to  pro- 
portion, do  not  themselves  produce  or  determine  it? 

What  then  does  determine  it? — what  but  the  conscious 
action  of  the  mind  judging  of  the  relative  measurements 
of  the  different  parts  of  this  image?  Notice  the  phrase- 
ology here — of  this  image.  Every  painter  knows  that  col- 
ors and  shadows  as  examined  close  at  hand  in  the  external 
world  often  differ  greatly  from  what  they  appear  to  be 
to  one  who  judges  of  them  by  the  image  on  the  retina. 
To  him  an  actually  checkered  surface  may  appear  to  be  of  a 
single  color,  and  a color,  owing  to  the  influence  of  sur- 
rounding hues,  may  appear  unlike  that  which  it  actually 
is.  The  same  fact  is  true  with  reference  to  outlines.  The 
eye  is  rounded  and  therefore  the  mind  behind  it  sees 
everything  through  a rounded  surface.  If  one  look  into  a 
convex  mirror  he  will  find  all  of  the  dimensions  of  the 
natural  world  slightly  altered.  As  a rule,  for  instance, 
the  straight  upward  lines  of  a square  object  with  its  base 
on  the  middle  line  of  the  mirror  will  appear  not  to  be 
parallel  but  to  approach  one  another.  The  effects  in  the 
mirror  merely  exaggerate  the  effects  already  exerted  upon 


PR  OP  OR  TION  MIS  UNDER  STOOD. 


25 


nature  by  the  rounded  formation  of  the  eye.  As  ap- 
plied to  natural  surroundings,  we  become  accustomed  to 
these  effects  and  never  judge  lines  to  be  curved  or  lacking 
in  parallelism  merely  because  they  are  so  in  the  image  on 
the  retina.  On  the  contrary,  unless  they  were  so  in  this 
image,  we  should  judge  the  lines  to  be  neither  straight  nor 
parallel.  Accordingly,  when  men  try,  as  in  drawing  a 
picture,  to  reproduce  the  appearance  of  such  an  image,  it 
becomes  important  for  them  to  carry  out  what  are  termed 
the  laws  of  linear  perspective.  These  are  laws,  as  will  be 
explained  in  Chapter  XIV.,  in  accordance  with  which  all 
the  outlines  of  an  artificial  image,  whether  drawn,  painted, 
carved,  or  constructed,  or  however  changed  in  size,  are 
made  among  other  things  to  sustain  somewhat  the  same 
relations  as  in  an  image  naturally  produced  on  the  retina. 

Notice,  moreover,  that  to  fulfil  these  laws  of  perspective 
so  as  to  make  this  artificial  image  correspond  to  the  image 
in  the  eye  is  one  thing;  and  that  to  make  the  respective 
dimensions  of  this  image  appear  to  fulfil,  each  to  each, 
the  laws  of  proportion  is  another  thing.  Yet  it  is  quite 
easy  and  natural  to  confound  the  two.  We  need  not  be 
surprised,  therefore,  to  find  them  almost  invariably  con- 
founded in  theories  of  proportion,  especially  in  those 
which  have  had  most  influence  in  causing  men  to  think 
that  the  subject  is  too  complex  and  mysterious  for  solu- 
tion. Those  who  have  advanced  these  theories  have 
failed  to  recognize  that  the  analogue  of  proportion  is  not 
harmony  but  rhythm.  Moreover,  as  rhythm  is  an  effect 
of  the  conscious  action  of  the  mind,  its  general  principles 
are  comparatively  easy  to  ascertain  ; and,  by  carrying  out 
the  analogies  suggested  by  them,  the  explanation  of  the 
effects  of  proportion  may  be  rendered  comparatively 
easy.  But  the  processes  through  which  the  ear  becomes 


26 


PROPORTION  AND  HARMONY. 


cognizant  of  the  harmonic  relations  between  musical  notes 
and  chords  are  difficult  to  ascertain,  for  the  very  reason 
that  the  mind  is  not  conscious  of  these  processes.  No 
wonder,  therefore,  that  a theory  identifying  with  them 
those  of  proportion  by  which  the  mind,  through  the  eye, 
becomes  cognizant  of  the  relations  existing  between 
spaces,  should  involve  difficulties.  Such  a theory  starts 
out  with  the  supposition  that  effects  of  proportion  end  in 
the  physical  senses,  whereas  they  are  recognized  only 
by  the  mind.  Afterwards,  when  the  theory  goes  on  to 
explain  these  effects,  of  course  it  can  do  this  only  so  far 
as  it  can  explain  other  physiological  effects.  But  these 
cannot  be  explained  except  through  hypothesis. 

Yet  this  theory,  as  has  been  said,  is  the  one  that  is 
usually  advanced.  It  is  true,  too,  that  it  is  supposed  to 
have  been  derived  from  the  Greeks;  and  that  the  Greeks 
are  acknowledged  to  have  had  a more  thorough  under- 
standing of  the  subject  than  any  other  people.  But  is 
the  theory  derived  from  the  Greeks?  Is  it  certain  that 
the  expressions  of  the  Greeks  with  reference  to  the  mat- 
ter have  been  properly  interpreted  ? The  Latin  writer  Vi- 
truvius tells  us  in  his  “ De  Architectural  book  iii.,  chapter 
i.,  that  they  called  proportion  not  harmony  but  analogy 
( avaXoyia ).  To  this  it  may  be  answered,  of  course,  that 
Pausanias,  in  chap.  xii.  of  the  Arcadia,  speaking  of  the 
beauty  of  the  stone  of  which  the  “ Theseum  was  composed, 
and  its  harmony  throughout,”  employs  the  word  harmony 
(dpptonog),  and  that  Plato,  too,  in  his  Republic,  says 
that,  “ as  the  eyes  seem  to  be  fitted  for  the  harmonious 
proportions  of  the  celestial  orbits,  so  the  ears  seem  to  be 
fitted  for  the  harmony  of  musical  intervals;  and  these 
seem  to  be  sister  sciences ; as  the  Pythagoreans,  indeed, 
affirm,  and  we  must  accord  with  them.” 


PROP  OR  TION  MIS  UNDER  S TO  OD. 


2 7 


This  use  of  terms,  however,  does  not  necessarily  mean 
all  that  is  attributed  to  it.  There  is  nothing  correspond- 
ing to  what  we,  at  least,  term  proportion  in  the  effects  of 
the  celestial  orbits,  or,  if  there  were,  did  we  ourselves 
choose  to  use  the  word  harmony  not  in  its  more  restricted 
technical  sense  as  applied  in  modern  times  merely  to  note 
or  color,  but,  as  the  Greeks  themselves  did,  as  meaning 
any  unity  whatever  produced  by  a blending  of  parts  or 
multiples  of  parts  according  to  mathematical  ratios,  then 
we  too  could  ascribe  harmony  not  only  to  note  or  color 
but  also  to  rhythm  ; and  if  to  rhythm,  of  course,  to  pro- 
portion. 

But  it  has  generally  been  supposed  that  the  Greeks 
meant  more  than  this,  that,  reversing,  to  say  the  least,  the 
natural  order  of  investigation,  they  determined  what 
should  be  the  conscious  action  of  the  mind  in  measuring 
spaces  from  an  examination  of  what  will  be  shown,  in 
Chapter  XX.  of  this  volume,  to  be  its  unconscious  action  as 
affected  by  conditions  underlying  the  effects  of  note  and 
color.  This  conception  of  the  Greek  method  is  at  the 
basis  of  the  theory  in  Peter  Legh’s  “ Music  of  the  Eye  ” ; 
as  well  as  of  that  in  Adolf  Zeising’s  work  “On the  Law  of 
Proportion  which  Rules  all  Nature.”  In  the  latter,  the 
relations  of  harmonic  tones  in  music  are  used  as  a basis 
for  the  construction  of  a “ Golden  Section,”  as  it  is  called. 
This  may  be  described  as  a measure  divided  into  parts, 
each  of  which  is  related  to  all  the  other  parts,  according  to 
some  simple  ratio  ; and  the  whole  is  represented  as  furnish- 
ing a standard  of  related  measurements  for  all  beautiful 
proportions.  The  theory  is  suggested  by  a not  wholly 
warranted  interpretation  given  to  an  obscure  passage  in 
Plato’s  “ Timaeus,”  in  which  there  is  mention,  indeed,  of 
divisions  of  a string  as  determining  proportions  ; but  also, 


28 


PROPORTION  AND  HARMONY. 


a little  farther  on,  of  angles  and  figures  as  determining 
them.  It  is  noteworthy,  too,  that  in  making  practical 
tests  of  this  golden  rule,  the  author  finds  fault  with  the 
Parthenon  because  it  does  not  conform  to  his  require- 
ments. But  the  Greeks  would  hardly  have  esteemed  this 
building  so  highly,  had  it  not  fulfilled  their  own  archi- 
tectural principles. 

D.  R.  Hay,  again,  attributes  to  suggestions  from  the 
ancients  the  whole  of  the  very  ingenious  and  interesting 
theory  in  his  essay  on  a “ System  of  Geometric  Propor- 
tion ” ; and  he  bases  this  theory  upon  the  same  hypothe- 
sis, namely,  that  “ the  division  of  space  into  an  exact 
number  of  equal  parts  will  aesthetically  affect  the  eye  in 
the  same  way  that  the  division  of  the  time  of  vibrations 
[by  which  he  means  the  vibrations  determining  the  pitch 
of  notes]  in  music  into  an  exact  number  of  equal  parts 
aesthetically  affects  the  mind  through  the  medium  of  the 
ear.”  James  P'ergusson,  also,  in  his  “History  of  Archi- 
tecture,” vol.  i.,  pt.  i,  bk.  iii,  chap,  ii,  sanctions  this  view. 
In  speaking  of  the  effects  of  the  ratios  employed  by  the 
Greeks,  he  says:  “Many  would  be  inclined  to  believe 
they  were  more  fanciful  than  real.  It  would,  however, 
be  as  reasonable  in  a person  with  no  ear  or  no  musical 
education,  to  object  to  the  enjoyment  of  a complicated 
concerted  piece  of  music  experienced  by  those  differently 
situated,  or  to  declare  that  the  pain  musicians  feel  from  a 
false  note  was  mere  affectation.  The  eyes  of  the  Greeks 
were  as  perfectly  educated  as  our  ears.  They  could  ap- 
preciate harmonies  which  are  lost  in  us,  and  were 
offended  at  false  quantities  which  our  dull  senses  fail  to 
perceive.  But  in  spite  of  ourselves  we  do  feel  the  beauty 
of  these  harmonic  relations,  though  we  rarely  know 
why.”  Nor  does  Fergusson  attempt  to  explain  the  reason. 


PROP  OR  TION  MIS  UNDER  STOOD. 


29 


F.  C.  Penrose,  also,  in  his  work  on  “ The  Principles  of 
Athenian  Architecture,”  implies,  in  many  expressions, 
his  adherence  to  this  theory.  So  too  does  W.  W.  Lloyd 
in  the  very  valuable  Appendix  accompanying  that  work 
as  published  by  the  Society  of  Dilettanti,  as  well  as  in 
his  equally  valuable  one  accompanying  C.  R.  Cockerill’s 
“Temples  at  /Egina  and  Bassae.”  While  Lloyd  does 
this,  however,  he  makes  an  important  concession.  “ In 
response  to  what  is  implied  in  these  expressions,”  he 
says  (Penrose’s  “ Prin.  of  Athen.  Arch.,”  Appendix,  p.  1 1 1), 
“ the  speculative  have  not  been  remiss  in  asserting  for 
architectural  harmony  as  close  a dependence  on  mathe- 
matics as  has  been  so  long  established  for  musical.  Ad- 
mitting the  justness  of  the  presumption  so  far,  I may  say, 
at  once,  that  my  own  conclusions  are  quite  at  variance 
with  what  is  often  the  next  presumption,  that  the  ratios 
of  the  diatonic  scale  have  any  special  value  as  realized  in 
architectural  forms.” 

What  ratios  do  have  value  in  the  Parthenon  he  tells  us 
in  the  following  language  {idem,  p.  112):  “It  will  be 
observed  that  the  ratios  2 : 7,  4 : 9,  and  9 : 14  have  respect- 
ively the  common  difference  between  their  terms  of  5. 
In  the  recited  order  the  terms  approach  towards  equal- 
ity, and  the  series  may  be  extended  by  insertion  of  inter- 
mediate and  other  ratios  having  the  same  characteristic. 
Thus  1:6,  2:7,  3 : 8,  4 : 9,  5:10,  etc.  It  will  be  found 
that  several  of  these  ratios  are  repeated  with  marked  in- 
tention.” And  what  if  they  are?  What  if  we  learn  even 
so  important  a fact  as  that,  in  the  Parthenon,  the  width 
of  the  column  was  to  that  of  the  whole  breadth  of  the 
front  as  5:81;  or,  as  Penrose  informs  us  in  his  “ Princi- 
ples of  Athenian  Architecture,”  that  the  ratio  of  the 
architrave  to  the  step  was  89:90?  It  is  evident  that, 


30 


PROPORTION  AND  HARMONY. 


for  any  practical  purpose,  unless  something  more  be  dis- 
covered— unless  some  deeper  principle  be  unfolded  which 
apparently  these  surface-facts  have  suggested  not  even  as 
a possibility  to  these  writers — an  architect  of  our  own 
time  can  derive  no  benefit  from  them.  Years  ago,  when 
the  author  of  this  book  was  in  college  and  studying  me- 
chanics, a subject  that  was  taught  by  compelling  the  class 
to  learn  by  rote  long  series  of  intricate  formulae,  a class- 
mate— John  H.  Denison — came  around  one  morning  and 
declared  that  now  he  understood,  as  never  before,  the 
object  of  our  study.  He  said  that  he  had  had  a dream. 
In  this,  he  had  found  himself  in  an  oriental  country. 
They  were  erecting  a gigantic  building.  But,  to  complete 
it,  they  needed  to  raise  from  the  ground  an  enormous 
stone  with  which  to  crown  its  summit.  The  king  and  his 
ministers  and  all  the  people  had  assembled  to  see  this 
done.  But  all  efforts  were  in  vain.  Finally,  impelled 
by  a happy  inspiration,  he  himself  shouted  at  the  top  of 
his  voice  the  longest  of  these  formulae  that  he  had  been 
learning.  Instantly,  lifted  by  the  magic  of  this,  which 
proved  to  be  an  incantation,  the  great  stone  ascended  to 
its  place,  while  all  the  people  prostrated  their  forms  be- 
fore the  man  who  had  shouted  the  formula,  and  the 
heiress  to  the  throne  was  led  forward  to  be  presented  to 
him  in  marriage.  As  ordinarily  conceived,  the  connection 
between  the  ratios  used  by  the  Greeks  and  the  practical 
applications  of  them  to  aesthetic  requirements  is  about 
as  close  as  was  that  between  formulae  and  performance  in 
the  conception  of  the  students  for  whose  benefit  this 
dream  was  told.  As  has  been  intimated,  the  funda- 
mental reason  for  such  a lack  of  connection  is  a mis- 
understanding of  the  nature  of  the  effects  of  proportion, 
arising  from  allying  them  with  those  at  the  basis  not  of 


PROP  OR  TION  MI  SUNDERS  POOD. 


31 


musical  rhythm  but  of  harmony.  Of  course,  as  already 
intimated,  there  is  an  analogy  between  the  mathematical 
ratios  that  determine  results  in  harmony  and  in  rhythm 
or  proportion  ; and  this  fact  may  at  times  render  plausi- 
ble, often  apparently  conclusive,  each  of  the  various  theo- 
ries mentioned  in  this  chapter.  But  the  point  is  that  all 
these  theories  fail  to  take  into  consideration  a fact  which 
modifies  the  effects  of  their  strict  application.  This  fact 
is  the  difference  between  actual  measurements  and  appar- 
ent measurements,  between  measurements  as  they  are  in 
an  external  object  and  as  they  seem  to  be  to  the  eye 
perceiving  them  from  a distance. 


CHAPTER  IV. 


PROPORTION  AS  BASED  UPON  COMPARISONS  OF  APPARENT 
MEASUREMENTS : STRAIGHT  LINES  AND 
RECTANGULAR  FIGURES. 

Proportion  and  Perspective  Both  to  be  Studied,  but  Separately — Perspective 
Considers  the  Difference  between  Subjective  Effects  and  Objective  Ar- 
rangements Occasioning  Them— Proportion  Considers  Appearances, 
Perspective  the  Method  of  Producing  them — Comparison  or  Likeness  is 
the  Basis  of  Proportion — Illustrations — Small  Numbers  Necessary  to  the 
Recognition  of  Ratios — Outlines  Indicating  like  Subdivisions  an  Aid 
to  this  Recognition — The  Principle  Applicable  to  Comparisons  between 
both  Rectilinear  and  Rectangular  Measurements — Between  Adjacent 
Figures  as  Wholes — Hay’s  Theory. 

r I "O  say  that  proportion  is  one  thing,  and  perspective 
another  thing,  does  not  free  the  man  who  would  have 
an  intelligent  view  of  the  former  subject  from  the  necessity 
of  paying  attention  to  the  latter.  It  merely  makes  it  im- 
perative for  him  to  separate  the  two,  and  study  each  by 
itself.  This  we  shall  now  proceed  to  do,  devoting  Chapters 
IV.  to  XIII.  to  proportion,  and  those  immediately  fol- 
lowing them  to  perspective.  Meantime,  before  unfolding 
further  the  latter  subject,  enough  has  been  said  to  indicate 
to  the  reader  that,  when  treating  of  proportion,  we  are 
treating  of  effects  produced  upon  the  mind  by  conditions 
that  appear  to  exist  in  the  object  perceived,  but  which 
do  not  necessarily  exist  there  in  reality.  That  is  to  say, 
though  in  nature  the  measurements  of  an  object  may  ful- 
fil the  requirements  of  proportion,  they  may  not,  owing 


32 


33 


34 


PROPORTION  AND  HARMONY. 


to  the  operation  of  the  laws  of  perspective,  fulfil  them  in 
the  image  which  this  object  produces  on  the  retina;  and, 
vice  versa , though  in  nature  the  measurements  may  not 
fulfil  the  requirements  of  proportion,  they  may,  neverthe- 


FIQ.  7.— KAFFIR  STATION,  AFRICA. 

See  pages  40,  162. 


less,  owing  to  the  operations  of  the  laws  of  perspective, 
fulfil  them  in  this  image.  In  short,  as  applied  to  propor- 
tion as  to  many  other  artistic  features,  a work  of  art, 


PROPORTION  AND  PERSPECTIVE. 


35 


whether  a painting,  a statue,  or  a building,  has  to  be 
judged  by  what  may  be  termed,  and  is,  in  this  sense,  its 
subjective  effect  after  it  has  begun  to  influence  the  eye 
and  mind. 


FIG.  8.— TYPE  OF  AN  ASSYRIAN  SQUARE. 
See  pages  40,  43,  44,  162. 


Is  it  necessary  to  argue  that  this  truth  is  not  generally 
recognized  ? When  a man  with  a yardstick  is  measuring, 
close  at  hand,  the  parts  of  the  Parthenon,  then,  according 
to  the  generally  accepted  representation,  he  is  studying 
proportion.  But  he  is  really  doing  nothing  of  the  sort. 
He  is  studying  proportion,  when  he  is  standing  at  a distance 
from  the  building  and  noticing  the  parts  of  it,  which,  from 


36  PROPORTION  AND  HARM  ON  V. 

that  distance,  appear  to  fulfil  the  requirements  of  those 
comparative  measurements  which  proportion  necessitates. 

When  he  is  close  against  the 
building  with  his  yardstick,  he  is 
more  apt  to  be  learning  the  dif- 
ferences between  measurements 
as  they  are,  and  as,  from  a dis- 
tance, they  appear  to  be,  the  con- 
sideration of  which  differences 
and  the  methods  of  obviating 
them  furnish  the  subject-matter 
not  of  proportion  but  of  perspec- 
tive. In  the  case  of  the  Greeks, 
too,  as  we  shall  find,  the  princi- 
ples of  the  latter  were  applied  in 
order  to  produce  distant  appear- 
ances of  proportion  not  only,  but  also  of  height,  breadth, 


FIQ.  10.— TEMPLE  OF  THESEUS,  ATHENS. 

See  pages  40,  44,  116,  156,  163,  164,  168,  170,  175,  188,  189,  193,  196, 
201,  210,  2x1,  218,  219,  220,  221,  224,  252. 

straightness,  parallelism,  and  other  effects,  which,  in  addi- 
tion to  those  of  proportion,  were  deemed  desirable.  As 


FIG.  9. --MEDIAEVAL  CASTLE. 

See  pages  40,  145,  162. 


PROPORTION  AND  PERSPECTIVE. 


37 


said  in  the  last  chapter,  a chief  reason  why  the  require- 


FIG.  11.— ST.  STEPHENS,  CAEN,  NORMANDY. 

See  pages  42,  44,  154,  163,  166,  170,  175,  226. 

ments  of  proportion  are  supposed  to  be  involved  in  im- 
penetrable mystery,  and  why,  therefore,  the  neglect  of  them 


38 


PROPORTION  AND  HARMONY. 


in  our  own  day  is  supposed  to  be  excusable,  is  traceable 
to  this  confounding  of  these  two  entirely  different  ob- 
jects of  inquiry. 

Now  with  a clear  apprehension  that,  at  present,  we  are 
to  consider  merely  proportion,  which  has  to  do  with  the 


FIQ.  12. — CANTERBURY  CATHEDRAL,  FROM  SOUTHWEST. 

See  pages  42,  163,  175,  226. 


measurements  which  the  mind  makes  of  appearances ; 
and  that  only  by  and  by  are  we  to  consider  perspective, 
which  has  to  do  with  the  arrangements  producing  appear- 
ances, let  us  confine  attention  for  a time  to  the  former 
subject.  In  proportion,  it  is  the  apparent  measurements 
of  certain  divisions  and  subdivisions  of  objects  that  are 
compared.  As  was  said  in  the  last  chapter,  these  measure- 


PROPORTION  MARKED  BY  LIKE  SUBDIVISIONS.  39 

merits  could  not  be  compared  unless  they  were  related  to 
one  another  according  to  ratios  expressible  in  small  num- 
bers. To  illustrate  this  fact  further,  as  well  as  to  in- 
dicate why  it  ts  a fact,  let  us  suppose  ourselves  to  be 
judging  of  the  relative  lengths  of  different  lines  or  sur- 


FIG.  13.— CENTRAL  CONGREGATIONAL  CHURCH,  BOSTON. 
See  page  42. 


faces,  or  of  different  divisions  of  the  same  line  or  surface. 
Our  task  will  evidently  be  easiest  when  the  numbers  are 
smallest  ; i.  e.,  when  the  two  lengths  compared  are  as  1:1, 
or  are  exactly  alike.  We  see,  therefore,  why  this  rela- 
tionship should  be  historically  the  earliest  form  and,  even 


40 


PROPORTION  AND  HARMONY 


in  our  own  day,  the  most  universal  in  which  the  tendency 
to  proportion  manifests  itself.  Notice,  as  already  indi- 
cated in  Chapter  II.,  the  equal  spaces  in  Figs.  1,  page  1 2, 
2,  page  12,  and  3,  page  12.  In  Fig.  6,  page  33,  notice  the 
equal  spaces  between  the  platforms.  In  Fig.  7,  page  34, 
notice  the  rude  but  similarly  equal  divisions  of  heights. 
In  the  specimen  of  early  civilized  architecture,  in  Fig. 
8,  page  35,  observe  the  equal  height  of  each  storey  and 


FIG.  14.— WILLESDEN  CHURCH,  NEAR  LONDON,  ENGLAND. 

See  pages  42,  154. 

the  equal  width  of  each  panel.  In  Fig.  9,  page  36, 
observe  the  equal  divisions  in  the  tower  considered  per- 
pendicularly. In  Fig.  10,  page  36,  observe  that  the 
columns  divide  the  sides  considered  horizontally  into 
approximately  equal  divisions,  as  do  also  the  foundation, 
entablature,  and  pediment  of  the  front  (see  Fig.  94, 


FIG.  15. -CHICHESTER  CATHEDRAL,  ENGLAND. 

See  pages  42,  43,  158,  163,  165. 


42 


PROPORTION  AND  HARMONY. 


page  183)  considered  perpendicularly.  Observe,  too,  the 
perpendicular  divisions  of  the  towers  in  Fig.  r r , page  37, 
and  the  horizontal  divisions  caused  by  the  buttresses  in 
Fig.  12,  page  38.  Fig.  13,  page  39,  shows  an  imitation  of 
this  last  method,  but  with  the  number  of  spaces  of  ex- 
actly the  same  width,  too  small  to  produce  the  desired 
rhythmic  or  proportional  effect.  Figs.  77,  page  150,  81, 
page  1 55,  82,  page  156,  show  like  measurements  both  verti- 
cal and  horizontal.  In  Fig.  1 5,  page  41,  the  ornamenta- 
tion of  the  spire  divides  it  so  that  each  part  of  it  seems  to 
be  of  the  same  height  as  the  upper  part  of  the  tower  be- 
neath it,  and  in  Fig.  14,  page  40,  the  tower  seems  to  be  of 
the  same  width  as  the  church.  This  universal  use  of  the 
ratio  1 : 1 has  been  illustrated  thus  fully,  because  it  is  im- 
portant for  the  reader  to  understand  that  it  is  the  ele- 
mentary relationship  which  is  recognized  in  proportion, 
and,  as  such,  is  at  the  basis  of  all  its  developments. 

If,  however,  the  relationship  be  not  that  of  1 : 1,  the 
next  easiest  to  recognize  is  that  of  1:2,  as  between  the 
first  of  the  upper  and  lower  lines  at  the  left  of  Fig.  16. 


FIG.  16.— LINES  IN  PROPORTION. 

See  pages  42,  43. 

Nor  is  it  difficult  to  recognize  the  relationship  of  1:3,  as 
between  the  second  pair  of  lines  in  this  figure,  or  of  2 : 3, 
as  between  the  third  pair.  But  it  is  evident  that  as  the 
values  of  the  numbers  representing  the  ratios  increase, 
these  become  less  recognizable  ; as,  for  instance,  when 
they  are  as  4:5  or  as  5 : 7,  as  between,  respectively,  the 
fourth  and  fifth  pairs  of  lines  in  this  Fig.  16.  When,  at 
last,  we  get  to  a relationship  that  can  be  expressed  only 


PROPORTION  MARKED  BY  LIKE  SUBDIVISIONS  43 


by  large  numbers  like  10:  11,  or  15  : 16,  the  mind  is  no 
longer  able  to  recognize  even  its  existence. 

There  is  a way,  however,  in  which  one  may  be  made  to 
recognize  it,  even  when  represented  by  comparatively 
large  numbers.  This  is  when,  in  accordance  with  the 
elementary  process  in  proportion  of  putting  like  with 
like,  the  wholes  of  the  forms  that  are  to  be  compared  are 
measured  off  into  like  subdivisions.  For  instance,  it  is 
far  more  easy  to  recognize  the  relationship  of  4:5,  or  at 
least  that  there  is  such  a relationship,  when  it  is  expressed 
as  in  Fig.  17,  below,  than  when  it  is  expressed  as  in  lines 
like  those  in  Fig.  16,  page  42.  Accordingly,  like  subdivi- 
sions when  they  are  indicated  as  in  Fig.  17  may  show  not 


FIG.  17.— LINES  SUBDIVIDED  TO  INDICATE  PROPORTION. 

See  page  43. 

only  the  relationship  that  each  subdivision  sustains  to 
each  other  subdivision  that  measures  the  same  as  itself, 
but  the  relationship  also  that  whole  series  of  subdivisions 
sustain  to  other  series  of  them,  which,  as  series,  do  not 
measure  the  same.  Thus,  the  panels  in  the  lower  storey 
in  the  Assyrian  tower  in  Fig.  8,  page  35,  show  that 
the  whole  length  of  each  storey  sustains  a certain  definite 
relationship  to  the  whole  length  of  each  other  storey. 
So,  too,  the  ornamental  divisions  in  the  spire  in  Chi- 
chester Cathedral  (Fig.  15,  page  41)  show  that  the  whole 
spire  sustains  an  exact  relationship  of  3 : 1 to  the  square 
part  of  the  tower  visible  below  it  ; and  the  divisions  in 
the  towers  of  St.  Sulpice,  Fig.  82,  page  156,  suggest  that 
their  whole  height  sustains  a relationship  of  2 : I to  the 
height  of  the  central  part  of  the  building. 


44 


PROPORTION  AND  HARMONY. 


We  are  told  by  W.  W.  Lloyd  in  his  “ Memoir  on 
the  Systems  of  Proportion,”  published  with  Cockerill’s 
“Temples  of  SEgina  and  Bassas,”  page  64,  that  all  the 
architectural  quantities  as  made  proportionate  were  esti- 
mated by  the  Greeks  chiefly  in  two  ways  : by  rectilinear 
proportions,  or  by  divisions  of  one  continuous  straight 
line  ; and  by  rectangular  proportions,  or  a comparison 
of  length  and  breadth,  height  and  width,  etc.,  at  right 
angles.  We  have  considered  the  first  of  these  ways.  In 
considering  the  second,  we  can  expect,  of  course,  no 
change  in  principle.  In  case  the  lines  to  be  compared 
form  adjacent  sides  of  a rectangle,  the  ratio  between 
the  lines  must  be  recognizable  in  the  degree  in  which 
it  can  be  expressed  in  small  numbers,  1 : 2,  2 : 3,  3 14,  etc. 
Or,  if  comparatively  large  numbers  be  necessitated,  they 
can  still  be  recognized  in  the  degree  in  which  certain 
marks  suggest  them  to  the  eye  ; or,  if  not  the  numbers 
themselves,  at  least  the  fact  that  they  exist  and  represent 
ascertainable  ratios.  Notice  this  Fig.  18,  representing 


FIG.  18.— FIGURES  WITH  LINES  SUBDIVIDED  TO  INDICATE  PROPORTION. 

See  pages  44,  263. 


3 : 5 and  4:7.  As  applied  in  actual  construction  also, 
observe  Fig.  8,  page  35  ; and  the  like  horizontal  or  verti- 
cal divisions  in  Figs.  10,  page  36,  1 1,  page  37,  77,  page  150, 
81,  page  155,  and  82,  page  156. 


RECTILINEAR  AND  RECTANGULAR  PROPORTIONS.  45 


Of  course,  this  method  of  making  lengths  and  breadths 
seem  in  proportion  in  the  same  figure  can  make  them 
seem  so  in  adjacent  figures  ; in  other  words,  it  can  make 
one  figure  as  a whole  seem  in  proportion  to  another 
figure.  If,  in  such  cases,  the  figures  be  rectangles,  they 
may  be  similar  in  width,  and  then  their  relationships  may 
be  determined  by  the  ratios  of  their  heights,  as  in  the  first 
three  rectangles  at  the  left  of  Fig.  19.  Or  if  the  rect- 
angles be  similar  in  height,  their  relationships  may  be 
determined  by  the  ratios  of  their  widths,  as  in  the  fourth, 
fifth,  and  sixth  rectangles  in  the  same  figure  Or,  if  the 


FIG.  19.— RECTANGLES  IN  PROPORTION. 
See  page  45. 


rectangles  be  similar  neither  in  width  nor  in  height,  their 
relationships  may  still  be  determined  by  the  ratios,  each 
to  each,  of  both  these  respective  dimensions,  as  in  the 
seventh,  eighth,  and  ninth  rectangles  in  Fig.  19. 


FIG.  20.— HAY’S  METHOD  OF  DETERMINING  PROPORTIONAL  RELATIONS 
OF  RECTANGLES. 

See  page  46. 


4 6 


PROPORTION  AND  HARMONY. 


D.  R.  Hay,  in  his  “ Science  of  Beauty  and  Laws  of 
Geometric  Proportion,”  makes  the  proportions  of  rectan- 
gles to  one  another  depend  upon  the  ratios  of  the  angles 
described  by  lines  drawn  from  corner  to  corner  as  in  Fig.  20, 
page  45.  There  may  be  something  in  this  ; but  mainly 


FIG.  21.— HAY’S  RECTANGLES  CORRESPONDING  TO  THE  MUSICAL  SCALE. 

See  page  47. 

for  a reason  which  Mr.  Hay  does  not  state.  This  is  the 
influence  which,  in  all  acts  of  vision,  angles  of  this  kind 
have,  owing  to  the  way  in  which,  according  to  the  laws  of 
perspective,  the  straight  lines  are  brought  together  at  a 


RECTILINEAR  AND  RECTANGULAR  PROPORTIONS.  47 


vanishing  point.  See  page  233,  also  Fig.  102,  page  235. 
It  is  possible  that,  in  order  to  cause  lines  on  a rounded 
retina  to  appear  to  be  of  like  lengths,  we  should  compare 
them  by  comparing  the  angles  to  which  they  are  similarly 
related,  not  at  one  corner  of  the  figure,  as  Mr.  Hay  does, 
but — what  would  practically  produce  the  same  result — - 
at  the  centre  of  the  figure.  Mr.  Hay,  carrying  out  the 
theory  mentioned  on  page  28,  holds  that  all  rectangles, 
as  well  as  all  figures  that  may  be  regularly  described  in 
such  rectangles,  are  harmonious,  in  case  the  angles  that 
he  mentions  bear  the  same  relations  to  one  another  as  do 
the  strings  of  musical  notes  that  form  harmonics  ; in  other 
words,  if  these  angles  be  to  one  another  as  I : 2,  2 : 3,  3 : 4, 
4 : 5,  5 : 6,  etc.  According  to  him,  the  rectangle  in  Fig.  21, 
page  46,  indicated  by  /,  corresponding  to  do  of  the  musical 
scale,  would  form  an  harmonic  with  that  marked  j,  or  5, 
or  8,  corresponding  respectively  to  me,  sol,  and  do  of  the 
musical  scale.  So  the  rectangles  marked  4,  6,  and  8 would 
form  harmonics,  because  corresponding  respectively  to 
the  fa,  la,  and  do  of  the  musical  scale. 


CHAPTER  V. 


PROPORTION  AS  BASED  UPON  COMPARISONS  OF  MEAS- 
UREMENTS IN  CURVED  AND  COMPLEX  FIGURES. 

Complex  and  Irregular  Figures  Shown  to  be  in  Proportion  by  Comparing 
each  with  some  Simple  and  Regular  Figure — Regular  Figures  as  Com- 
pared with  Rectangles — Importance  of  Having  the  Rectangles  Visible 
— The  Choir  of  Ely  Cathedral — Illustrating  the  Influence  of  Sugges- 
tion in  Outlines — The  Use  of  Figures  not  Rectangular  as  Standards  of 
Comparison  between  Complex  Figures — Aid  Afforded  by  Straight  Lines 
to  the  Perception  of  Proportion  in  Complex  Curves — Illustrations — Inti- 
mate Connection  between  Proportion  as  thus  Manifested  and  Harmony 
of  Outline— Curved  Circles,  Ellipses,  Used  as  Standards  of  Comparison 
between  Complex  Figures — Application  of  this  Method  to  the  Human 
Figure. 

CO  far  we  have  considered  only  straight  lines  and  rect- 
angular figures.  Of  course,  there  are  other  figures, 
and  they  form  a vast  majority,  that  are  not  composed  of 
straight  or  rectangular  or  even  regular  outlines.  It  is 
evident  that  to  compare  these  figures  together,  especially 
when  for  different  reasons  they  differ,  is  extremely  diffi- 
cult ; not  only  so  but  that  it  is  impossible,  unless  all  can 
be  shown  to  be  allied  to  some  simpler  and  more  regular 
figure  which  can  serve  as  a standard  of  measurement. 
This  simpler  figure,  which  is  just  as  essential  to  the  deter- 
mining of  like  space-dimensions  in  shape  as  a yardstick 
is  to  the  determining  of  like  lengths,  may  be  either  actually 
outlined  at  the  time  of  comparing  the  measurements  or 
only  ideally  imagined.  But  whether  actually  outlined  or 
not,  on  the  principle  that  things  equal  to  the  same  thing 

48 


PROPORTION  IN  IRREGULAR  FIGURES. 


49 


are  equal  to  one  another,  all  other  figures  inscribed  in 
this  simpler  figure  and  that  touch  all  its  sides  can,  for  this 
reason,  be  recognized  as  being  related.  See  Figs.  22, 
23,  and  24. 


/ \ 

FIG.  22.— FIGURES  RELATED  BECAUSE  INSCRIBABLE  IN  THE  SAME  SQUARE. 

See  page  49. 


7 1 

L 2 


FIG.  23.— FIGURES  RELATED  BECAUSE  INSCRIBABLE  IN  THE  SAME  RECTANGLE. 
See  page  49. 


FIG.  24.  — FIGURES  RELATED  BECAUSE  INSCRIBABLE  IN  THE  SAME  OR 
A RELATED  FIGURE. 

See  pages  49,  50. 


There  is  a deduction  from  this  fact  made  by  Mr.  Hay, 
which  well  illustrates  the  erroneous  influence  of  an  unten- 
able theory,  his  theory  being,  as  stated  on  page  28,  that 
“ the  division  of  space  into  an  exact  number  of  equal 
parts  will  aesthetically  affect  the  eye  in  the  same  way 
that  the  division  of  the  time  of  vibrations  \i.  e.,  the  vibra- 
tions determining  pitch]  in  music  into  an  exact  number 
of  equal  parts  aesthetically  affects  the  mind  through  the 


50 


PROPORTION  AND  HARMONY. 


medium  of  the  ear.”  He  says  that  any  regular  figures 
inscribable  in  one  rectangle  are  related  to  other  figures 
inscribable  in  another  rectangle  precisely  as  the  two  rec- 
tangles themselves  are  related.  Thus  the  same  relation 
that  the  first  and  second  drawings  in  this  Fig.  25,  sus- 

□ (moo  a /\  x x 

FIG.  25. — FIGURES  RELATED  BECAUSE  INSCRIBABLE  IN  FIGURES  IN  PROPORTION. 

See  pages  50,  51. 

tain  each  to  each,  is  respectively  sustained  also  by  the 
third  and  fourth,  the  fifth  and  sixth,  and  the  seventh  and 
eighth.  With  reference  to  this,  it  will  be  observed  that 
the  statement,  however  accurate  in  certain  cases,  does  not 
include  that  which  is  essential  to  render  it  accurate  in  all 
cases.  As  was  said  on  page  24,  proportion  is  an  effect  of 
a comparison  of  measurements  made  through,  but  not  by, 
the  physical  organs  of  sight.  It  is  made  by  the  mind. 
The  statement  that  two  things  are  in  proportion  being  a 
statement  of  what  seems  a fact,  because  apparent  to  the 
mind,  it  is  evident  that  any  surrounding  arrangements 
which  render  the  results  of  the  measurements  apparent, 
and  thus  interpret  them,  are  very  important  factors  in  pro- 
ducing the  effect.  Certainly,  the  first  three  forms  in  Fig. 
26,  when  they  are  separated  from  the  rectangles  in 


FIG.  26,— RELATIONSHIP  OF  FIGURES  AS  INDICATED  AND  AS  NOT  INDICATED. 

See  page  50. 


PROPORTION  IN  IRREGULAR  FIGURES. 


51 


which,  in  the  last  three  forms,  they  are  shown  to  be  in- 
scribable,  do  not  suggest  any  relationship  to  one  another. 
Nor  would  the  fifth  and  sixth  or  the  seventh  and  eighth 
forms  in  Fig.  25,  page  50,  were  it  not  for  the  rectangles 
in  the  first  and  second,  with  which  the  figure  shows  them 
to  be  connected.  Or,  to  indicate  the  practical  bearings 


FIG.  27.— CHATEAU  DE  RANDAU,  VICHY,  FRANCE. 
See  pages  51,  149,  164,  166. 


upon  art  of  this  remark,  it  is  conceivable  that  the  different 
triangles  described  by  the  pitch  of  the  gable-windows, 
roofs,  and  turrets  in  Fig.  27,  above,  would  all  be  found 
to  be  exactly  inscribable  in  rectangles  which,  according 
to  what  was  said  on  page  48,  are  in  proportion  to  one 
another.  But  because  the  rectangles  are  not  visible,  and, 
in  the  circumstances,  cannot  be  made  visible,  the  different 
triangles  do  not  seem  to  be  either  in  proportion  or  in  har- 
mony. In  this  regard,  they  have  a much  less  artistic 
effect  than  the  like  triangularity  of  the  shapes,  and  conse- 


/ 


52 


PROPORTION  AND  HARMONY. 


quent  parallelism  of  the  lines,  in  the  arrangements  con- 
nected with  the  roofs  and  turrets  in  Fig.  28,  page  53. 
Notice,  too,  how  the  rectangular  framings  into  which  are 
set  the  arched  doors  and  windows  in  the  middle  of  the 
front  of  the  building  in  Fig.  29,  page  54,  redeem  the 
whole  from  an  effect  of  incongruity  and  disproportion 
which,  otherwise,  might  characterize  it. 

In  fulfilment  of  the  same  principle,  it  will  be  observed 
that  the  like  rectangular  spaces  in  the  ornamentation  in 
the  screen  behind  the  upper  seats  in  Fig.  30,  page  55, 
reveal  that  both  the  rounded  outlines  in  its  lower  section 
and  the  pointed  outlines  in  its  upper  section  are  in  pro- 
portion. Notice  also  the  correspondence  between  the 
width  of  these  rectangular  spaces  and  the  width  of  each 
of  the  divisions  in  the  under  part  of  the  window  just  be- 
low the  ceiling,  indicating  a relationship  of  I : I to  these 
divisions,  as  well  as  of  1 : 2 to  the  divisions  in  the  middle 
large  arch  below  it.  Notice,  also,  the  apparently  like 
measurements  in  the  width  of  these  same  rectangular 
spaces  above  and  behind  the  seats  and  in  the  height  of 
the  mouldings  over  the  two  large  arches  rising  toward  the 
ceiling,  as  well  as  in  the  height  of  the  string-courses,  or 
cornices,  immediately  above  these  mouldings;  and  also  in 
the  height  of  the  ornamentation  which  is  immediately  in 
front  of  the  higher  seats.  Notice  again,  sustaining  a gen- 
eral ratio  of  about  3 : 1 to  the  measurement  just  mentioned, 
like  measurements  of  he  ight  in  that  which  is  between  the 
lower  edge  of  the  ornamentation  in  front  of  the  higher 
seats  and  the  floor  of  the  cathedral;  also  between  the 
upper  edge  of  this  ornamentation  and  each  highest  point 
reached  by  each  of  the  small  arches  above  it ; also  between 
this  latter  and  the  highest  point  reached  by  the  screen 
behind  the  stalls;  also  between  this  and  the  lower  edge  of 


FIG.  28.—  CHENONCEAU  CHATEAU,  FRANCE. 

See  pages  52,  166. 


54 


PROPORTION  AND  HARMONY. 


the  mouldings  over  the  lower  large  arch;  also — but  only 
approximately — between  the  upper  edge  of  these  mould- 
ings and  the  capital  of  the  column  from  which  the  middle 
large  arch  springs ; also  between  this  last  and  the  lower 
edge  of  the  mouldings  above  the  middle  large  arch  ; and 
also — but  here  too  only  approximately  — between  the 


FIQ.  29.— WALKER  MUSEUM,  CHICAGO  UNIVERSITY. 

“Cosmopolitan  Magazine.” 

See  page  52. 


upper  edge  of  these  mouldings  and  the  place  from  which 
the  arch  of  the  upper  window  springs.  Two  of  these  di- 
visions have  been  indicated  as  being  only  approximately 
of  the  same  height  as  the  rest.  With  reference  to  this  it 
may  be  suggested,  first,  that  to  one  looking  upward  from 
below,  as  alone  these  divisions  can  be  seen,  the  difference 
indicated  would  not  be  distinguishable,  and,  second,  that 
probably  few  looking  at  the  plan,  as  it  lies  before  one  in 
the  figure,  will  not  feel  that,  as  a whole,  it  would  be  more 
satisfactory  were  these  divisions,  instead  of  being  approxi- 
mately the  same,  actually  the  same;  will  not  feel,  in 
other  words,  that  the  general  arrangement  would  seem 


FIG.  30.— CHOIR  OF  ELY  CATHEDRAL,  ENGLAND. 

See  pages  52,  56,  57,  163,  166. 


55 


56 


PROPORTION  AND  HARMONY. 


more  satisfactory,  were  the  space  between  the  lower 
string-course  and  the  middle  arch  slightly  higher,  and  the 
ceiling  higher  above  the  upper  window,  and  rounder  In 
addition  to  what  has  been  said,  it  is  scarcely  necessary  to 
point  out  the  almost  infinite  instances  of  like  measurements 
in  the  minute  details  of  the  ornamentation  in  Fig.  30; 
or  how  often  these  details  are  made  to  fit  exactly  two, 
three,  four,  or  five  times,  as  the  case  may  be,  into  some 
larger  feature  of  which  they  are  constituent  members.  It 
is  enough  to  remark  that,  while  it  is  sometimes  supposed 
to  be  otherwise,  careful  observation  will  detect  that  the 
beauty  of  Gothic  as  well  as  of  Greek  architecture  is  vir- 
tually inseparable  from  the  minutest  fulfilment,  on  the 
part  of  their  architects,  of  these  elementary  principles  of 
proportion. 

This  Fig.  30,  page  55,  may  be  made  to  illustrate  two 
other  facts.  If  the  reader  will  glance  along  the  upper 
part  of  the  ornamentation  over  the  stalls  he  will  see  that 
in  many  places,  where  there  are  no  actual  horizontal  lines, 
the  outlines  are  so  arranged  as  to  suggest  these,  and, 
therefore,  through  them,  to  suggest  spaces  with  like 
measurements.  It  has  been  pointed  out  that,  when  two 
figures  are  related  because  of  their  relationships  to  related 
rectangles,  it  is  desirable  to  have  the  lines  of  these  rect- 
angles indicated.  Of  course,  in  many  cases  this  cannot 
be  done.  But,  though  not  indicated,  they  may  often  be 
suggested,  as  in  the  outlines  just  noticed.  At  other 
times,  as  in  the  outlines  of  plants  and  animals,  it  may 
seem  as  if  even  suggestion  were  impossible.  But,  as  we 
shall  find,  such  is  not  the  case  as  frequently  as  might  be 
supposed. 

The  other  fact  which  Fig.  30  may  be  made  to  illus- 
trate is  this.  It  will  be  observed  that  the  different  out- 


PROPORTION  IN  THE  HUMAN  FORM. 


57 


lines  and  divisions  in  the  large  arches  are  made  to  seem  in 
proportion  because  these  arches  themselves,  in  which  they 
are  framed,  are  in  the  main  alike.  In  other  words,  figures 
of  various  outlines  can  be  made  to  seem  to  be  in  propor- 
tion, when  they  are,  or  can  be,  framed  not  only  in  like 


FIG.  31.— LINES  AND  CURVES  INDICATING  PROPORTIONS  OF  A FORM  TAKEN 
FROM  PUTNAM’S  HANDBOOK. 

See  pages  15,  58,  59,  69,  72,  85,  87,  118,  120,  130,  131,  135,  137,  138, 
290,  291,  295. 

rectangles,  but  in  any  like  figures  whatever.  The  rectan- 
gle is  used  as  an  actual  or  ideal  standard  of  comparison 
merely  as  a matter  of  convenience.  It  is  comparatively 
easy  to  recognize  whether  or  not  straight  lines,  such  as 
form  its  sides,  are  of  the  same  lengths,  or  are  the  same 


53 


PROPORTION  AND  HARMONY. 


distances  apart,  or  have,  in  other  regards,  other  measure- 
ments that  are  in  proportion.  It  would  be  a mistake, 
however,  to  suppose  that  the  standard  of  measurement  is, 
or,  in  all  cases,  can  be  rectangular.  Take  the  human 
form.  It  is  ordinarily  divided  into  equal  parts  by  hori- 


FIG.  32.— LINES  AND  CURVES  INDICATING  PROPORTIONS  OF  A FORM  TAKEN 
FROM  PUTNAM’S  HANDBOOK. 

See  pages  15,  58,  59,  69,  85,  87,  118,  120,  130,  131,  135,  137,  290,  295. 

zontal  lines,  such  as  may  be  seen  in  Fig.  31,  page  57, 
and  Fig  32  ; and  these  lines  are  undoubtedly  an  aid  in 
determining  the  proportions.  But,  as  will  be  shown  on 
page  68,  effective  aid  may  be  afforded  by  circles  also, 


PROPORTION  IN  THE  HUMAN  FORM. 


59 


such  as,  in  this  book,  are  drawn  about  the  forms  in  these 
figures  not  only,  but  also  in  Figs.  35,  page  70;  36,  page 
7 1 i 37.  page  72  ; 45,  page  86  ; 62,  page  121  ; 72,  page  136; 
73.  Page  1 37  ! and  74,  page  139;  as  well  as  by  curves  of  a 
more  varied  character  described  on  pages  60,  61,  and  292. 
Notice  also  how  the  contours  of  all  the  human  forms  in  the 
products  represented  in  Figs.  55,  page  101  ; 75,  page  142; 
and  129,  page  359,  are  arranged  along  lines  of  like  curva- 
ture. Segments  of  curves,  like  those  drawn  about  the  fig- 
ures mentioned  in  the  sentence  before  the  last,  are  almost 
always  suggested  to  the  mind  when  looking  at  the  human 
figure  ; and  it  is  mainly,  perhaps,  by  likeness  in  these  that 
the  impression  is  conveyed — so  important  to  aesthetic 
effects — of  the  fufilment  of  similar  principles  both  in  shape 
and  in  measurement. 

But  while  this  is  true,  it  does  not  render  less  true  the 
fact  that  the  relationships  of  irregular  figures  are  rendered 
much  more  easy  to  recognize,  when  so  arranged  that  the 
measurements  of  their  parts  can  be  compared,  each  to 
each,  with  those  resulting  from  the  use  of  straight  lines. 
Notice  how  the  straight  lines  drawn  about  or  through  the 
outlines  in  Figs.  31,  page  57;  32,  page  58;  45,  page  86; 
62,  page  121  ; 63,  page  122;  69,  page  128,  facilitate  the 
recognition  of  like  divisions  of  spaces  in  these  outlines. 

A very  interesting  illustration  of  the  aid  afforded  by 
straight  lines  to  the  perception  of  the  fact  that  like  is  put 
with  like,  may  be  observed  in  Fig.  33,  page  60,  and  Fig. 
34,  page  61.  These  figures  contain  the  curve  which 
Ruskin,  in  his  “ Modern  Painters,”  vol.  iv.,  chapter 
xvii.,  page  5,  declares  to  be  the  most  common  in  nature. 
It  is  the  curve,  too,  certain  like  segments  of  which, 
as  indicated  in  the  paragraph  before  the  last,  furnish 
us  with  a standard  for  judging  of  shape  and  proportion 


6o 


PROPORTION  AND  HARMONY. 


in  the  human  form.  It  is  the  curve  which,  outlining 
limbs  of  different  lengths  and  breadths,  gives  a sugges- 
tion of  similarity  to  the  effects  of  the  contours  of  the  arms 
from  shoulders  to  elbows,  and  from  elbows  to  wrists;  of 
the  legs  from  hips  to  knees,  and  from  knees  to  ankles,  as 
well  too  as  of  larger  parts  of  the  frame,  as  from  shoulders 
to  heels,  and  also  from  hips  to  heels.  The  curve  is  one 
so  described  as  to  show  a constant  tendency  to  become 
straight,  although  never  becoming  straight.  In  Fig.  33, 


See  pages  59,  69,  294. 

the  angles  at  a,  b,  c,  d,  and  e are  in  each  case  the  same,  but 
the  line  a — b becomes  regularly  shorter  than  b — c , and  so 
on.  In  the  direction  of  g,  the  curve  a — g evidently  in- 
clines more  and  more  to  differ  from  the  requirements  of  a 
circle,  and  to  approximate  a straight  line.  In  Fig.  34,  page 
61,  the  distance  between  the  lines  A — a and  B — b and  C — c, 
etc.,  is  the  same,  but  the  curved  line  a — b becomes  regularly 
shorter  than  b — c,  and  so  on.  It  is  evident  that  in  this 
figure  the  curve  a — g,  while  constantly  approaching  the 
form  of  a straight  line,  can  never  become  one.  In  “The 


PROPORTION  IN  CURVES. 


61 


Genesis  of  Art-Form,”  page  283,  it  was  asked  why- 
curves  of  this  kind  are  seen  so  frequently  in  nature, 
and  why,  when  they  are  seen,  they  are  considered  es- 
pecially satisfactory  ? The  answer  suggested  was  that 
such  curves  necessarily  fulfil  the  requirements  of  the 
methods  developed  from  comparison ,‘  as  indicated  in 
the  chart  on  page  3.  In  the  first  figure,  the  angles 
at  a,  b,  c,  etc.,  are  the  same,  and  in  the  second  figure 
the  distances  between  the  lines  A — a,  B — b , C — c , 
etc.,  are  the  same,  while  the  differences  in  the  di- 
visions of  lines  in  both  figures  are  increased  or  di- 
minished according  to  the  same  degrees  or  ratios. 

The  principle  of  putting  like  measurements  with 
like,  therefore,  enters  into  the  formation  of  these 
curves,  notwithstanding  the  constant  tendency  that 
they  show  toward  a deviation  from  it.  Each  of 
the  curves,  too,  is  so  constructed  that  any  given 
part  of  it  may  be  magnified  so  as  to  represent 
exactly  f — g.  There  is  therefore  a sense  in  which 
these  curves  are  formed  in  accordance  with  the 
methods  indicated  in  the  chart  on  page  3,  under 
the  heads  not  only  of  comparison  and  repetition 
but  also  of  gradation , transition , and  progress' 

1 There  may  be  some  who  would  like  to  have  indicated 
here  the  exact  way  in  which  each  of  the  methods  of  compo-  y 
sition  mentioned  on  page  3 can  contribute  to  the  effects  of 
proportion.  In  “ TheGenesisof  Art-Form,”  all  these 
methods  were  said  to  result  from  the  effort  of  the 
mind  to  reduce,  in  order  to  understand  and  use,  the  d, 
variety  and  complexity  of  nature  to  some  form 
of  unity.  (Notice  that,  in  this  note,  the  words 
which  are  the  same  as  the  terms  used  for  the 
art-methods  in  the  chart  on  page  3 are'4  B cdefghijk 
italicized.)  The  means  of  attaining  this  F|Qt  34.— a CURVE  EXEMPLIFYING 
unity  was  said  to  be  classification,  which  is  a GRADATION. 

See  pages  59,  69,  294. 


62 


PROPORTION  AND  HARMONY. 


As  said  at  the  beginning  of  the  last  paragraph,  this 
illustration  with  its  many  straight  lines  will  suggest  the 
influence  of  these  lines  in  causing  a recognition  of  the 
fulfilment  of  the  principle  of  proportion  even  in  very 
subtle  and  complex  curves.  It  cannot  fail  to  be  ob- 
served, however,  that  these  straight  lines,  as  drawn  here, 

process  of  putting  into  the  same  groups  unlike  complex  wholes  on  the 
ground  that  they  are  alike  in  part.  Dogs  and  wolves,  for  instance,  are  not 
alike  as  wholes,  but  they  are  in  part.  So  scientific  zoology  puts  them 
together.  Buddhism  and  Christianity  are  not  alike  as  wholes,  but  they  are 
in  part.  So  scientific  religion  puts  them  together.  Art  deals  with  external 
appearances.  So  in  it,  partially  similar  sounds  or  shapes  are  put  together. 
But  if  they  must  be  put  together  in  such  ways  that  they  may  be  recognized 
to  be  in  part  alike,  it  is  necessary,  first  of  all,  that  they  be  arranged  in 
accordance  with  some  principle  of  order  exercised  sufficiently,  at  least,  to 
cause  the  confusion  of  mere  variety  to  be  counteracted  by  the  grouping.  As 
applied  to  objects  of  sight,  this  would  mean  that  no  artistic  effects  can  be 
produced  by  any  number,  say,  of  eyes,  ears,  fingers,  feet,  columns,  capitals, 
steps,  whatever  they  may  be,  when  lying  about  in  a disarranged  condition. 
Their  effects  as  related  to  proportion,  for  instance,  would  be  impossible  to 
determine  before,  by  means  of  orderly  grouping , the  eyes,  ears,  fingers,  feet, 
columns,  capitals,  or  steps  had  been  put  into  the  places  for  which  they  were 
designed.  Such  a grouping , moreover,  can  be  effective  in  revealing  the  pro- 
portions so  as  to  be  easily  recognized  in  the  degree  only  in  which  it  is  con- 
ducted on  the  principle  of  putting  like  factors  side  by  side  in  such  a way  as 
to  facilitate  an  exercise  of  comparison.  That  which  enables  the  mind  to 
perceive  that  one  feature  is  not  larger  or  smaller  than  it  should  be,  and  is, 
therefore,  in  proportion,  is  the  fact  that  it  is  of  the  same  measure  as  another 
feature,  or  as  a part  of  some  other  feature  with  which,  owing  to  the  place  in 
which  it  is  grouped , it  can  readily  be  compared. 

This  is  the  fundamental  fact  with  reference  to  proportion.  That  it  has 
not  been  brought  to  light  and  emphasized,  is  little  less  than  marvellous. 
But  whether  we  look  at  an  animal,  a man,  or  a building,  we  recognize  its 
members  to  be  in  proportion  in  the  degree  only  in  which  we  find  large  num- 
bers of  them  that  have  like  measurements,  and  others  that  are  exact  multi- 
ples of  these.  It  is  ordinarily  supposed  that  we  have  discovered  the 
proportions,  as  they  are  termed,  when  we  have  found  one  or  two  factors 
related  to  one  another,  say  as  4 : 9,  or  7 : 12,  or  9 : 14.  This  is  an  error. 
As  has  been  already  shown,  we  have  not  discovered  the  proportions, 


PROPORTION  IN  CURVES. 


63 


are  an  afterthought,  and  that  the  connection  between 
them  and  the  effect  of  this  kind  of  a curve  is  of  a more 
occult  character  than  that  which  has  been  said  to  be 
ascribable  to  proportion.  That  is  to  say,  it  is  not  of  a 
character  which  can  be  considered  to  be  distinctively 
apparent.  But,  in  connection  with  this  thought,  the 

until  we  have  found  not  one  or  two  but  many  factors,  each  of  which  is  re- 
lated to  many  others,  and  all  of  which  are  often  related  to  all  the  others  by 
the  same  or  multiples  of  the  same  ratios. 

Even  when  this  has  been  done,  however,  inasmuch  as  no  object  is  com- 
posed of  features  all  of  which  are  absolutely  alike,  there  is  necessarily 
involved  a recognition  of  contrast  also.  In  fact  it  is  largely  because  of  con- 
trast in  substances,  as  when  wood  is  used  together  with  stone,  or  in  qualities, 
as  when  red  color  is  used  together  with  blue,  that  it  is  important  that  feat- 
ures should  compare  in  shapes,  sizes,  or  quantities,  as  in  proportion.  Just 
as  in  the  arts  appealing  to  the  ear,  the  mind  can  perceive  a reason  why 
sounds  compare,  though  produced  by  very  different  instruments  and  at  very 
different  degrees  of  pitch, — including,  sometimes,  the  very  inharmonious 
effects  of  drums  and  cymbals, — if  only  all  these  sounds  together  seem  to  be 
constituent  factors  of  one  general  form  of  rhythm,  so  with  the  various  effects 
appealing  to  the  eye,  in  case  they  seem  factors  of  one  general  form  (A propor- 
tion. The  mind  can  readily  recognize  a basis  of  comparison  between  them, 
in  case  they  be  grouped  so  that  like  measurements  are  apparent.  But  in 
measurements  there  are  often  contrasts  too.  In  such  cases,  as  in  others  like 
them  mentioned  in  Chapters  II.  to  V.  of  “The  Genesis  of  Art-Form," 
effects  of  unity  may  still  be  secured  by  grouping  the  factors  in  such  ways 
that  the  contrasting  features,  where  they  cannot  compare  with  others,  shall 
complement  them, — as,  for  instance,  the  head  of  a turtle  complements  its 
tail,  and  the  head  of  a man  his  feet,  or  his  arms  his  legs,  or  the  roof  of  a 
house  its  foundation.  It  must  not  be  forgotten,  however,  that,  as  comparison 
is  the  fundamental  method,  principality  must  in  all  cases  be  given  to  this 
method,  while  subordination  must  be  given  to  the  method  of  contrast.  At 
the  same  time  balance  may  be  applied  to  many  such  features  as  have  been 
mentioned,  as  well  as  to  like  eyes,  ears,  hands,  feet,  and  windows  and 
towers.  These,  though  they  cannot  be  placed  together  in  the  centre  of  a 
product,  may  all  be  grouped  so  as  to  occupy  corresponding  places  at  either 
side  of  the  centre,  and  thus  may  all  be  made  to  be  essential  factors  entering 
into  the  general  unity  of  its  organic  form. 

These  statements  are  enough  to  indicate  briefly  in  what  sense  proportion 


64 


PROPORTION  AND  HARMONY. 


reader  needs  to  be  reminded  that  the  developments  re- 
sulting from  putting  like  with  like  according  to  the  meth- 
ods indicated  in  the  chart  on  page  3,  are  manifested  not 
only  in  rhythm  and  proportion  but  also  in  harmony, 
whether  of  sound  or  sight,  the  difference  between  the  first 
two  and  the  latter  being  that  in  the  former  we  are  con- 

is  a development  of  the  earlier  of  the  methods  treated  in  “ The  Genesis  of 
Art-Form,”  and  mentioned  in  the  chart  on  page  3.  But  let  us  go  on.  The 
three  methods  in  which,  according  to  the  discussion  in  that  book,  co?npari- 
son  manifests  itself,  are  by  way  of  congruity,  of  repetition , and  of  consonance. 
As  applied  to  proportion,  comparison  by  way  of  congruity  would  lead  to 
having  the  like  divisions  of  spaces,  large  or  small,  or  tending  to  either  ex- 
treme, representative  of  the  sentiment.  By  this  is  meant,  as  explained  in 
Chapters  III.  to  VI.  of  “Painting,  Sculpture,  and  Architecture  as  Repre- 
sentative Arts,”  that  such  qualities  as  weight,  importance,  firmness,  dignity, 
or  nearness,  whether  in  an  animate  or  inanimate  form,  would  be  indicated 
by  relative  largeness  ; and  that  such  qualities  as  lightness,  unimportance, 
flexibility,  grace,  and  remoteness,  would  be  indicated  by  relative  smallness. 
The  thick  wrists,  ankles,  fists,  feet,  and  neck  of  a pugilist,  or  the  heavy 
columns  and  entablatures  of  a Greek  temple,  mean  one  thing,  and  the  slight 
wrists,  ankles,  fingers,  feet,  and  neck  of  a dancer,  or  the  light  shafts  and 
pointed  arches  of  a Gothic  cathedral,  mean  another  thing. 

Owing  to  the  variety,  however,  always  characterizing  every  object  in 
nature,  there  are  frequently  delicate  features, — eyes,  ears,  nose,  mouth,  fin- 
gers, and  limbs,  as  the  case  may  be,  even  upon  a pugilist  ; as  well  as  deli- 
cate carvings  and  mouldings  amid  the  weightier  effects  of  a Greek  temple  ; 
while  opposite  characteristics  may  be  seen  in  the  form  of  the  dancer  or  of 
the  Gothic  temple.  These  exceptions,  though  introducing  incongruity , 
may  nevertheless,  by  similarity  in  measurements,  in  a single  direction,  as  in 
length  alone,  or  in  breadth  alone,  be  in  proportion , and  together  with  the 
features  which  are  wholly  congruous , enhance  the  proportional  comprehen- 
siveness of  the  general  result. 

When  assuming  postures,  to  suggest  thought  through  a representation  of 
arrested  motion,  as  well  as  to  meet  the  requirements  of  the  laws  of  perspec- 
tive, the  forms  of  men  and  animals,  as  also,  for  other  reasons,  those  of  land- 
scapes and  buildings,  have  to  be  arranged,  as  explained  in  Chapters  X.  and 
XI.  of  “ The  Genesis  of  Art-Form,”  with  reference  to  one  central-point  of 
view.  Vitruvius,  in  his  “ De  Architecture, ” tells  us  that,  with  the  Greeks, 
“ every  posture  of  action,  as  in  walking,  wrestling,  boxing,  was  mathemati- 


PROPORTION  IN  CURVES. 


65 


scious  of  the  elements  that  are  put  together,  and  in  the 
latter  we  are  not  conscious  of  them,  and  can  only  become 
aware  of  them  as  a result  of  scientific  demonstration.  At 
the  same  time,  there  are  both  sounds  and  sights  which  are 
in  the  border-land,  as  we  may  term  it,  between  these  two 
conditions.  For  instance,  in  the  deepest  bass-note  of  the 

cally  studied  ; and  the  line  of  the  centre  of  gravity  was  carefully  marked  ; 
when  the  position  of  each  limb  and  the  breadth  of  each  portion  of  the  whole 
frame,  first  conceived  to  be  located  in  a circumscribed  circle  or  square,  and 
then  in  an  enclosed  cube  or  square,  was  measured  with  the  greatest  ac- 
curacy ” ; and  we  shall  find  in  Chapter  XIV.  that  an  analogous  method  was 
practised  by  the  same  people  in  determining  the  proportions  of  architecture. 
These  facts  are  noteworthy  because  it  is  evident  that,  while  such  arrange- 
ments about  a central-point , in  connection  with  the  extremities,  treated  as 
in  what  is  called  in  the  chart  on  page  3 setting , do  not  change  the  neces- 
sity for  like  measurements  or  multiples  of  measurements,  they  do  change, 
decidedly,  the  actual  measurements.  A foreshortened  limb  represented  as 
thrust  forward  toward  us  from  a picture  must  be  actually  drawn  much 
shorter  than  another  of  exactly  the  same  size  in  nature.  Otherwise  we 
should  say  that  the  foreshortened  limb  was  out  of  proportion.  Thus  we  see 
that  proportion  has  to  do  with  central-point  and  setting ; and  an  analogous 
connection  will  be  shown  in  Chapter  XIV.  to  exist  between  it  and  the  same 
principles  of  perspective  as  applied  to  architecture. 

Again,  when  members,  especially  those  connected  with  organized  life  as 
in  animals  and  human  beings,  are  arranged  in  accordance  with  the  require- 
ments of  central-point  and  setting , it  is  evident  that  the  recognition  of 
likeness  in  measurements  or  multiples  of  measurements,  may  be  greatly 
facilitated  through  the  method  of  parallelism . Even  when  a body  is  in  re- 
pose, similar  general  lines  of  direction,  either  horizontal,  as  in  those  of  the 
eyes,  mouth,  and  shoulders,  or  vertical,  as  in  those  of  columns  or  of  window 
sides,  enable  us  easily  to  compare  their  measurements.  The  method  is  needed 
still  more  when  objects  are  not  in  repose,  when  limbs  are  apparently  thrust 
out  at  all  angles  from  a body,  or  when  roofs  and  spires  project  from  a build- 
ing. Then,  only  parallelism  between  two  or  more  directions  can  enable  us 
readily  to  estimate  the  relative  measurements  ; and  only  many  instances  of 
parallelism  in  the  features  at  either  side  of  a form,  can  enable  us  to  per- 
ceive clearly  that  these  are  well  balanced.  And  it  is  only  when  parallelism, 
as  thus  revealing  balance , has  had  its  perfect  work,  that  we  can  say  that  a 
form  is  in  proportion  in  the  sense  in  which  we  use  the  word  when  we  refer 
5 


66 


PROPORTION  AND  HARMONY. 


organ  we  can  distinguish  vibrations  allying  its  effects  to 
those  of  rhythm  almost  as  clearly  as  we  can  distinguish 
pitch  allying  them  to  those  of  harmony.  So  in  the  case 
of  this  particular  curve,  a reason  for  the  use  of  which  is 
indicated  here  in  accordance  with  the  principles  of  propor- 

to  what  is  termed  its  symmetry.  See  Chapters  X.  and  XI.  of  “The 
Genesis  of  Art-Form.” 

The  connection  between  proportion  and  comparison  by  way  of  repetition , 
alteration , alternation , hardly  needs  to  be  mentioned.  By-and-by  it  will  be 
shown  how  many  like  measurements  there  are  both  in  bodies  animate  and 
inanimate,  and  in  buildings,  facilitating  thus  the  recognition  of  proportion 
not  only  by  way  of  repetition  but  of  massing.  Of  course,  however,  few  of 
these  features  do  not  manifest  also  alteration.  Moreover,  as  many  of  them 
are  absolutely  unique  like  noses  and  mouths  amid  eyes  and  ears,  or  doors 
amid  windows,  and  spires  amid  roofs,  they  exemplify  interspersion.  Fre- 
quently, too,  as  do  fingers  and  columns  with  their  intervening  spaces,  they 
exemplify  alternation , and,  less  frequently  perhaps,  as  intertwining  limbs  in 
active  figures,  and  as  interlacing  arches  and  groinings  of  roofs,  they  exemplify 
complication,  and,  when  lines,  though  interrupted,  are  continued,  they  ex- 
emplify continuity.  See  “ The  Genesis  of  Art-Form,”  Chapter  XIV.  In 
connection  with  none  of  these  methods,  however,  can  the  different  features 
composing  the  form  be  said  to  be  in  proportion,  except  so  far  as  in  length 
or  in  breadth  or  in  some  other  regard  they  apparently  manifest  like  measure- 
ments or  like  multiples  of  these. 

Features  are  said  to  be  in  proportion,  in  the  sense  of  fulfilling  the  method 
of  consonance,  when  they  exemplify  like  principles  of  formation.  These  are 
exemplified  when  like  measurements  or  multiples  of  these  appear  to  separate 
or  determine  different  parts  of  their  shapes.  If,  for  instance,  there  be  a 
similarity  of  shape  between  the  upper  line  of  the  eyebrows  and  the  lower 
line  of  the  hair  on  the  forehead,  we  admire  what  we  term  the  proportions 
of  the  forehead.  Or  if,  in  postures,  there  be  given  from  a side  view  a 
similar  bend  to  the  elbow  and  to  the  hip,  or  to  the  wrist  and  to  the  knee, 
a bend,  i.e.,  of  such  a kind  that  many  curves  and  angles  seem  similar,  and 
many  lines  seem  parallel— in  this  case  too  we  admire  what  we  term  the 
proportions,  by  which  we  mean  the  similar  or  symmetrical  measurements  of 
the  spaces  between  the  respective  curves,  angles,  and  lines  ; and  an  analogous 
principle  evidently  applies  to  square,  round,  or  angular  window-caps,  arches, 
and  gables.  Even  where  there  is  not  consonance  but  dissonance,  proportion 
may  still  appear  to  be  a characteristic,  in  case  the  products  manifest  the 


PROPORTION  IN  CURVES. 


67 


tion, — this  explanation  will  not  prevent  another,  and  per- 
haps a better  one,  which  will  be  given  on  page  292,  and 
which  ascribes  it  to  the  principles  underlying  harmony  of 
outline. 

Figs.  31  to  34  have  shown  how,  when  of  equal  length 

same  general  measurements  between  the  features,  even  though,  specifically 
considered,  these  be  differently  shaped,  as  is  the  case  where  there  is  the  same 
distance  from  the  hair  of  the  forehead  to  the  middle  of  the  eye-space,  that 
there  is  from  the  latter  to  the  nostrils,  or  from  the  nostrils  to  the  tip  of  the 
chin.  See  page  86.  So  too  with  the  facade  of  a building  in  which  the  forms 
considered  in  themselves  are  unlike.  They  may,  nevertheless,  be  separated 
by  like  spaces.  See  Chapters  IX.  and  X.  The  same  likeness  of  spaces  may 
cause  proportion  where  there  is  interchange , as  when,  descending  from  the 
two  eyes  and  ears  through  the  one  nose  but  with  two  nostrils,  a transition  is 
made  to  a single  feature,  the  mouth  and  chin  ; or  when,  descending  from 
arched  windows  in  an  upper  storey  of  a building  through  straight  window-caps 
but  an  arched  doorway  in  a lower  storey,  a transition  is  made  to  uniformly 
straight  window-caps  and  door-caps  in  a basement.  Interchange , as  thus 
interpreted,  and  also  as  explained  in  Chapter  XVII.  of  “ The  Genesis  of 
Art-Form,"  is  merely  one  of  a general  series  of  links  that  we  have  in  grada- 
tion ; but,  as  related  to  proportion,  this  last  method,  as  well  as  that  of 
abruptness , has  chiefly  to  do  with  arrangements  through  which,  by  means  of 
curves  or  angles  (see  “The  Genesis  of  Art-Form,”  pages  282-9),  z.  transi- 
tion is  made  in  the  progress  of  the  general  outline  from  one  measurement 
or  series  of  measurements  to  another  or  others.  No  artist  hesitates  to  speak 
of  the  proportions  of  the  human  figure  as  determined  not  merely  by  measure- 
ments, as  is  the  case  primarily,  but  also  (see  Chapter  VIII.)  by  the  curves  or 
angles  through  which  a member  with  a certain  form  is  made  to  pass  into 
one  with  another,  as,  for  instance,  the  breast  into  the  waist,  the  waist  into 
the  hips,  the  calf  into  the  ankle,  or  the  ankle  into  the  foot  ; and  the  same 
is  true  of  the  phrases  used  in  order  to  express  the  way  in  which  columns  are 
made  to  pass  into  arches,  and  arches  into  groinings,  or  intoother  ornamental 
features  of  a ceiling  above  them.  Inasmuch,  also,  as  light  and  shade  and 
color  have  to  do  with  producing  the  apparent  effects  of  form  upon  the  eye, — 
that  is,  in  causing  them  to  appear  as  curves,  angles,  or  squares, — it  will  be 
seen,  as  was  said  on  pages  6 and  7,  that  just  as  there  is  a virtually  in- 
separable connection  between  rhythm  and  harmony  as  appealing  to  hearing, 
so  too  there  is  a similar  connection  between  proportion  and  harmony  as 
appealing  to  sight. 


68 


PROPORTION  AND  HARMONY. 


or  separated  by  equal  distances,  straight  lines  drawn  about 
or  through  forms  facilitate  the  recognition  of  the  fact  that 
certain  segments  of  curved  outlines  are  in  proportion. 
As  has  been  said,  these  straight  lines  with  or  without 
rectangles  are  used  for  this  purpose  as  a matter  of  con- 
venience. It  is  hardly  necessary  to  add  that  the  same 
conditions  might  sometimes  cause  the  standard  for  judg- 
ing of  the  proportions  of  adjacent  outlines  to  be  some- 
thing else  than  straight  lines,  or  than  any  combinations  of 
them,  as  in  squares,  triangles,  or  rectangles.  As  applied, 
for  instance,  to  almost  all  curved  lines,  this  standard 
would  be  some  regular  curve,  as  in  an  ellipse  or  a circle. 
Of  these  two,  the  latter  may  be  said  to  furnish  in  some 
regards  a standard  of  comparison  the  most  satisfactory  of 
any.  The  circle  is  more  regular,  and  thus  more  in  accord- 
ance with  the  fundamental  principle  of  proportion  than  is 
even  the  square.  Every  segment  of  a regular  circumfer- 
ence illustrates  a like  degree  of  curvature,  and  is  at  a like 
distance  from  the  centre,  as  well  as  from  a segment  of  the 
circumference  exactly  opposite  itself.  The  ellipse,  too, 
though  not  so  regular  as  the  circle,  is  sufficiently  regular 
for  practical  purposes.  See  the  dotted  lines  especially  in 
the  two  upper  drawings  in  Fig.  120,  page  285-  In  the 
ellipse  the  opposite  sides,  though  illustrating  contrast 
by  way  of  direction,  illustrate  comparison  also  by  way  of 
complement.  See  the  chart  on  page  3.  Besides  this,  as 
D.  R.  Hay  says  in  his  “Ornamental  Geometric  Diaper 
Designs  as  Applied  to  the  Decorative  Arts,”  the  ellipse 
“possesses  that  essential  constituent  of  beauty,  variety. 
Its  outline  being  formed  by  two  radii,  one  of  which  is 
continually  decreasing  while  the  other  is  increasing,  it  im- 
perceptibly varies  from  an  oblate  to  an  acute  curve,”- — 
a method  of  variation  not  essentially  different  in  prin- 


PROPORTION  IN  CURVES. 


69 


ciple,  as  will  be  noticed,  from  that  which  was  shown  on 
page  61,  to  be  fulfilled  in  the  curves  in  Figs.  33  and  34. 
For  the  reasons  just  stated,  either  the  circle  or  the  ellipse 
may  be  made  a standard  of  comparison  by  which  to  judge 
of  the  relative  measurements,  or — what  is  the  same  thing 
— the  proportions  of  contours  drawn  about  it  or  within 
it  ; and,  of  course,  in  case  outlines  are  curved  a curved 
standard  is  much  more  satisfactory  than  one  that  is  rect- 
angular. Attention  has  already  been  directed  to  the 
suggestions  of  like  segments  of  circles  such  as  are  made 
to  describe  the  chief  curves  in  the  foremost  outlines  of 
the  human  form  in  Figs.  31,  page  57,  and  32,  page  58. 
There  is  a reason  for  the  use  of  these  circles  as  a stand- 
ard of  measurement  derived  from  the  physiological  re- 
quirements of  the  eye,  especially  in  binocular  vision. 
This  reason  will  be  found  unfolded  in  Chapter  XVI.  Here 
it  is  sufficient  to  say  that  the  circumference  of  each  of 
the  two  circles  in  the  same  horizontal  plane  represents 
the  sphere  of  the  distinct — not  entire — vision  of  one  eye, 
and  that  when  all  the  circumferences  of  the  circles  de- 
scribed about  the  same  figure  are  the  same,  the  eyes  are 
supposed  to  be  focussed  for  distinct  vision  at  exactly  the 
same  distance.  At  a certain  distance  from  the  form,  for 
instance,  all  the  circles  are  of  one  size,  but  nearer  than 
this  all  of  them  are  of  another  size. 

All,  too,  are  attached  in  this  book  to  figures  drawn  not 
by  the  author  but  by  others  to  represent  what  they  sup- 
posed to  be  approximately  perfect  proportions.  Is  it  not 
remarkable  that  such  like  circles  outline  so  many  general 
features  of  the  contour  when  viewed  from  the  distance 
represented  in  Figs.  35,  page  70,  and  37,  page  72,  and  also 
so  many  particular  features  of  the  same  when  viewed 
from  the  distance  represented  in  Fig.  36,  page  71  ? Similar 


7o 


PROPORTION  AND  HARMONY. 


circles  would  have  been  described  about  the  statues  de- 
picted in  this  volume,  had  not  the  pose  of  these  been 
necessarily  such  as  in  most  cases  to  throw  the  limbs 
slightly  out  of  an  upright  position.  But  any  one  who 
will  go  over  any  representations  of  the  human  figure  with 


FIG.  35.— CIRCLES  DRAWN  ABOUT  A FORM  TAKEN  FROM  PUTNAM’S 
HANDBOOK.  SIDE  VIEW. 

See  pages  15,  59,  69,  87,  134,  135,  141,  290,  295. 


compasses  will  be  surprised  to  find  how  large  a part  of 
a segment  of  exactly  the  same  circle  fits  either  the  bend 
of  the  calf,  forearm,  thigh,  abdomen,  chest,  or  back.  If 
then  his  experience — say  at  a bathing-place — causes  him 
to  recall  the  aesthetic  influences  of  such  formations  as  a 
long  arm  or  leg  combined  with  great  leanness,  or  a small 


PROPORTION  IN  CURVES. 


71 


chest  combined  with  an  abnormally  large  abdomen,  he  will 
find  upon  reflection 
that  the  effects  of  dis- 
proportion, while  at- 
tributable partly  to 
association,  are  also 
attributable  partly  to  a 
recognition  of  an  ab- 
sence of  like  curves. 

Or,  to  illustrate  this 
fact  from  a contrary 
condition,  everybody 
admires  a small  ankle 
and  a good-sized  calf. 

Yet  the  moment  the 
calf  becomes  so  large 
proportionately  as  to 
interfere  with  the  sug- 
gestions of  a like  curve 
in  this,  and  in  the  out- 
lines of  the  hip,  almost 
everybody  is  conscious 
of  receiving  a sugges- 
tion of  disproportion. 

Withreference  tothese 
circles  drawn  about  the 
forms,  it  will  be  no- 
ticed too  that  in  the 
case  of  a man  there  is 
a like  degree  in  which 
the  two  horizontal  cir- 

r . FIG.  36.— CIRCLES  DRAWN  ABOUT  HAY’S  IDEAL 

cumferences  separate,  MAN  SIDE  V1EW 

being  as  much  nearer  See  pages  15, 59, 69, 72, 87, 133, 134. 135, 

2 go,  295. 


72 


PROPORTION  AND  HARMONY. 


together  at  the  shoulders  than  at  the  hips  as  they  are  nearer 
together  there  than  at  the  calves.  (See  Figs.  31,  page  5 7 ; 
36,  page  7 1 ; and  73,  page  137.)  In  the  case  of  a woman,  the 
circles  seem  to  be  very  nearly  at  the  same  distance  apart 
at  the  hips  as  at  the  shoulders.  (See  Fig.  3 7 ; and  Fig.  74, 
page  139.)  Whatever  the  arrangements  may  be,  how- 
ever, it  is  evident  that,  as  applied  to  these  as  well  as  to 


FIG.  37.— CIRCLES  DRAWN  ABOUT  HAY’S  IDEAL  WOMAN.  SIDE  VIEW. 

See  pages  59,  69,  72,  87,  134,  295. 


others  that  will  be  mentioned  hereafter,  we  may  draw  the 
general  conclusion  that  the  proportions  of  human  figures 
and,  probably,  of  all  natural  figures,  may  be  said  to  con- 
form to  certain  straight,  rectangular,  or  circular  stand- 
ards of  measurement  which,  or  the  ratios  between  which, 
may  be  conveniently  compared. 


CHAPTER  VI. 


PROPORTION  IN  LANDSCAPES,  PLANTS,  ANIMALS,  AND 
THE  SURROUNDINGS  OF  HUMAN  FORMS. 

Outlines  and  Figures  Used  as  Standards  of  Comparison  in  Measure- 
ments— Can  be  Used  even  in  Connection  with  Accurate  Imitation  of 
Nature — Application  of  the  Principle  to  Landscape — To  Forms  of 
Vegetable  and  Animal  Life — To  the  Arranging  of  the  Surroundings 
of  the  Human  Form — In  Stained-Glass  Windows — In  Clothing — 
Neglect  of  this  Opportunity — The  Mind’s  Satisfaction  in  a Partial 
Application  of  the  Principle — Surrounding  Arrangements  in  Connec- 
tion with  no  Clothing. 

TN  the  preceding  chapter  it  was  shown  that  simple  out- 
lines and  figures,  such  as  characterize  regularly  con- 
structed triangles,  squares,  rectangles,  circles,  ellipses,  etc., 
may  be  used  as  standards  of  comparison  through  which  to 
determine  the  relative  space-dimensions  of  complex  and 
more  or  less  irregular  outlines  and  figures.  It  was  said 
also  that  these  simpler  outlines  and  figures  described 
through  or  about  the  more  complex  ones  may  be  either 
actually  outlined  or  merely  ideally  imagined.  Of  course, 
in  all  cases  they  can  be  actually  outlined  by  the  artist 
during  the  preparatory  stages  of  his  work.  But  it  is  not 
of  these  that  we  are  now  speaking,  but  of  their  results  and 
of  the  methods  of  recognizing  the  proportions  in  the 
product,  which  is  often  a complex  and  more  or  less 
irregular  figure.  In  forms  imitating  nature,  as  represented 
in  painting  and  sculpture,  it  might  be  supposed  that 
any  simpler  outlines  or  figures  revealing  the  proportions 


73 


74 


PROPORTION  AND  HARMONY. 


must,  in  every  case,  be  left  to  be  imagined.  In  other  words, 
it  might  be  supposed  that  no  such  outlines  or  figures 
could  be  made  apparent  in  connection  with  the  repre- 
sentations of  hills,  valleys,  rivers,  trees,  plants,  animals,  or 
human  beings. 

Yet  why  should  this  be  supposed  ? Natural  speech  is 
not  always  rhythmical,  at  least  not  in  that  higher  sense 
in  which  it  is  also  metrical.  Yet  a dramatic  poet,  in  his 
artistic  representation  of  speech,  may  make  it  so.  In  the 
same  way,  why  may  not  a painter  or  sculptor,  whether  or 
not  a form  or  collection  of  forms  manifest  proportion  in 
nature,  make  it  do  so  in  his  artistic  treatment  ? The 
main  requisite  of  proportion,  as  we  have  found,  is  to  have 
some  apparently  like  standard  of  measurement  into  which 
certain  parts  or  sets  of  parts  in  an  object  of  sight  are 
divided  ; and  there  are  innumerable  methods,  not  involv- 
ing any  lack  of  exactness  in  imitation,  through  which  this 
result  may  be  attained.  Take  a mountain  scene.  A se- 
lection of  one  point  of  view  only  a hundred  feet  away 
from  another  may  entirely  change  the  suggestion  of  like 
divisions  afforded  by  the  lines  of  distant  and  nearer  ridges, 
of  snow  or  flora  of  different  characters,  and  of  the  borders 
of  lakes  or  rivers.  Or  take  a scene  involving,  apparently, 
much  greater  irregularity,  as  in  Fig.  38,  page  75.  Upon 
first  glancing  at  this,  one  may  think  that  there  is  neither 
need  nor  evidence  of  any  regard  for  proportion  in  it. 
But  if  what  has  been  said  thus  far  in  this  volume  be  true, 
effects  of  proportion,  aesthetically  considered,  are  always 
important  ; and  an  absence  of  them  will  always  exert 
some  influence,  even  though  the  spectator  may  not  be 
conscious  of  the  source  of  it.  With  this  thought  in 
mind,  let  us  see  if  we  can  find  any  evidence  of  a regard 
for  proportion  in  this  particular  painting.  Recalling  that 


FIG.  38.— THE  CANAL  BY  COROT. 

See  pages  74-77.  363.  365,  369- 


76  PROPORTION  AND  HARMONY. 

the  measurements  for  which  we  are  in  search  need  to  be 
alike  not  in  the  object  itself  but  in  the  appearance  which 
it  presents,  and  beginning  at  the  right  margin,  notice  the 
same  apparent  distance  between  it  and  a part  of  the  bush 
near  the  bottom  of  the  picture ; then  the  same  distance 
between  this  bush  and  the  first  tree  to  the  left  of  it ; then 
notice  about  half  this  same  distance  (1  : 2)  between  this 
tree  and  another  to  the  left  of  it  ; then  once  more  notice 
the  whole  of  the  distance  first  mentioned  between  this  other 
tree  and  the  next  tree  to  the  left ; then  the  same  distance 
between  this  last  tree  and  the  white  form  of  the  man  ; also 
between  this  and  the  left  side  of  the  bright  water-space; 
also  between  this  last  and  the  left  side  of  the  dark  water- 
space  ; also  between  this  last  and  the  end  of  the  boat ; then 
apparently  the  same  distance,  at  the  extreme  rear,  be- 
tween the  line  of  tall  trees  and  the  darker  bank  at  the 
left  of  them  ; also  the  same  between  the  beginning  of  this 
darker  bank  and  the  beginning  of  a still  darker  bank  to 
the  left  of  it  ; also  the  same  between  this  last  and  one  of 
the  two  stakes  on  the  river’s  bank  ; then,  after  an  interval 
of  about  half  this  distance  (1:2),  another  stake,  and  finally 
the  same  distance  as  that  separating  the  most  of  the  ob- 
jects mentioned  between  this  second  stake  and  the  left 
margin.  Besides  this,  notice  other  subsidiary  sets  of  like 
distances — for  instance,  the  four  and  one  half  like  dimen- 
sions into  which,  by  the  man’s  form  and  the  water-shadows, 
the  top  of  the  boat  seems  to  be  divided  ; also  the  five  and 
one  half  like  distances  between  the  tall  trees  and  the  left 
margin  indicated  by  the  general  outlines  of  the  small 
trees  at  the  rear  ; again  notice  another  like  distance  sepa- 
rating the  lower  margin  of  the  picture  from  the  water-end 
of  the  boat,  also  this  latter  from  the  lower  water-line  of 
the  bank  at  the  rear,  and  this  latter  again  from  the  top  of 


PROPORTION  IN  LANDSCAPES. 


77 


the  small  tree  above  the  bank.  Not  less  apparent  is  still 
another  like  distance  separating  the  lower  margin  of  the 
picture  from  the  bank  at  the  rear  of  the  water,  and  this 
again  from  the  top  of  the  tree  a little  to  the  left  of  the 
centre  of  the  picture,  and  this  tree-top  again  from  the 
upper  margin.  Another  like  distance  can  be  observed 
too  between  the  lower  margin,  the  white  shoulders  of  the 
man,  the  white  line  at  the  top  of  the  foliage,  and  the 
white  sky  appearing  under  the  leaves  of  the  trees.  Notice, 
again,  the  smaller  subsidiary  divisions  in  the  arrangements 
of  the  banks  and  their  shadows  at  the  rear.  Once  more 
as  an  aid  to  effects  of  proportion,  because  allying  the 
whole  to  regularity,  observe  also  the  parallelism  of  the 
trunks  of  the  high  trees  and  the  concentration  of  radiating 
lines  at  the  left  of  the  centre, — lines  formed  by  shadows, 
banks,  or  foliage,  but  all  together  entering  unmistakably 
into  the  general  effect.  Nor  can  we  consider  it  without 
design  that  the  light  and  dark  effects  in  the  picture  seem 
to  be  distributed  in  very  nearly  equal  quantities.  So 
much  for  the  evidences  of  proportion  in  this  picture, 
which  has  been  selected  for  the  very  reason  that,  at  first, 
it  might  not  be  supposed  to  contain  any  such  evidences. 
Yet  they  are  there.  Nor,  in  connection  with  them,  is 
there  the  slightest  suggestion  of  artificiality.  The  paint- 
ing accurately  represents  nature,  and  nature  deprived  of 
none  of  its  variety.  But  if  the  artistic  representation  did 
not  fulfil  the  requirements  of  proportion,  it  might  be  no 
more  entitled  to  be  considered  a work  of  art  than  would 
be  a poem,  if  devoid  of  rhythm. 

Unlike  the  outlines  of  inanimate  nature,  those  of  vege- 
table and  animal  life  are  always  proportional  in  themselves. 
Trees  and  bushes  as  wholes,  as  also  their  trunks,  limbs, 
and  leaves,  invariably  suggest  similar  measurements,  or, 


78 


PROPORTION  AND  HARMONY. 


at  least,  approximately  similar  measurements,  in  that 
they  are  balancing , complementary , or  parallel , as  on  op- 
posite sides  of  triangles,  squares,  circles,  ellipses,  or  their 
combinations.  See  the  chart  on  page  3 ; also  the  note 
beginning  on  page  61.  This  similarity  in  measurement 
is  sufficiently  suggested,  as  in  the  shape  of  a tree  and 
its  branches,  or  of  a leaf  and  its  veinings,  in  Fig.  39, 
below,  and  of  quadrupeds,  birds,  and  fishes,  in  Fig. 
122,  page  289.  What  most  concerns  the  student  of  art  is 
the  application  of  the  principle  to  the  human  form,  both 
because  it  is  this  to  which,  necessarily,  artistic  representa- 
tion is  mainly  confined,  and  because,  being  the  most  com- 
plex of  all  forms,  it  is  the  one  necessitating  requirements 
of  proportion  that  are  the  most  difficult  to  explain. 


FIG.  39.— RADIATION  IN  NATURAL  FORMS. 

See  pages  78,  288. 


Of  the  human  form,  it  seems  logical  to  begin  by  saying 
that,  as  usually  represented,  it  is  almost  always  possible  to 
suggest  the  proportions  through  a use  of  outlines  surround- 
ing it,  as  in  shrubbery,  upholstery,  drapery,  or  clothing. 
For  instance,  take  the  outlining  conditions  of  pictures 
produced  upon  stained  glass,  especially  in  windows. 
Such  windows  are  always  constructed  on  a network  of 
bars  which  cannot  be  hidden  ; and  these  necessitate  di- 
viding whatever  is  represented  on  the  glass  into  certain 


HUMAN  PROPORTIONS. 


79 


parts.  See  Fig.  40,  on  this  page. 
Why  has  it  never  occurred  to 
artists  to  have  these  bars  divide 
human  forms,  when  crossing 
them,  into  parts  of  like  longitud- 
inal dimensions?  Straight  lines, 
as  intimated  on  page  58,  cannot 
give  us,  perhaps,  the  most  im- 
portant indication  of  the  meas- 
urements determining  the  pro- 
portions of  the  human  form. 
But  such  lines  can  give  us  some 
indication,  and,  so  far  as  they  do 
this,  the  artist,  alive  to  his  op- 
portunities, will  utilize  them,  it 
being  an  elementary  principle  in 
art  that  its  necessary  limitations 
should  be  made  to  add  to  its 
effectiveness. 

These  bars  in  windows  of 
stained  glass  furnish  art  excep- 
tional opportunities.  Like  ones 
are  afforded  in  almost  every  other 
case  in  which  the  human  form 
is  represented.  But  how  seldom 
does  the  thought  of  utilizing 
them  occur  to  the  painter  or 
sculptor,  not  to  speak  of  the 
originator  of  styles  of  clothing? 
It  is  sometimes  supposed  that 
these  latter  need  fulfil  no  aesthetic 
principles, — that  men  will  think 
beautiful  any  style  to  which  they 


FIG.  40.— OLD  GLASS  OF  14TH 
CENTURY. 

See  page  79. 


8o 


PROPORTION  AND  HARMONY. 


have  become  accustomed.  But  they  will  not  think  it 
beautiful — whatever  word  they  may  use  in  order  to  ex- 
press their  thought  of  it ; at  best,  they  will  merely  think 
it  fitting,  because  it  is  conventional;  and  for  the  same 
reason,  too,  they  may  think  any  other  style  inappropriate. 
But  in  some  way,  which  possibly  they  cannot  explain, 
perhaps  not  even  recognize,  life  for  them  will  be  deprived 
of  certain  legitimate  aesthetic  influences,  the  presence  of 
which  might  enrich  their  experience.  This  statement 
applies  not  only  to  the  use  of  form  and  color,  but  also  of 
proportion.  How  easy  it  would  be  to  cause  the  cut  of 
the  garments  to  reveal  the  four,  five,  six,  or  eight  parts 
of  equal  lengths  into  which  the  height  of  the  well  propor- 
tioned body  is  divisible  ! A line  below  the  knee,  whether 
of  skirt  or  breeches  ; a line  at  the  middle,  whether  of  gir- 
dle or  waistcoat ; a line  in  the  centre  of  the  breast,  whether 
of  bodice  or  vest,  together  with  other  lines,  always  divide 
the  figure  satisfactorily.  These  lines,  as  intimated  on  page 


FIQ.  41.— COSTUMES  DIVIDING  HUMAN  FORMS  PROPORTIONATELY. 

See  pages  80,  81. 

58,  may  not  indicate  that  which  is  most  important  in 
the  proportions  of  the  human  figure.  But  so  far  as  they 


PROPORTION  IN  CLOTHING. 


8l 


go,  they  furnish  a method  of  representing  proportion  with 
which  the  art  of  the  costumer  cannot  afford  to  dispense. 

Notice  this  fact  as  illustrated  in  certain  universally  ad- 
mired costumes  of  different  periods,  as  sketched  in  Fig. 
41,  page  80.  The  first  figure  to  the  left  shows  a division 
into  four  equal  parts  ; the  next  figure  to  the  right  of  it, 
a division  into  five  equal  parts  ; and  the  next  two  figures, 
divisions  into  six  equal  parts.  This  next  Fig.,  42,  shows 


See  pages  81,  82. 

costumes,  fashionable  and  not  fashionable,  in  which  there 
are  no  suggestions  of  equal  divisions.  A glance  at  the  re- 
sults will  be  enough  to  reveal  their  unaesthetic  effects,  and 
that  they  are  due  to  a lack  of  likeness  in  measurements. 

Why  is  the  influence  of  the  arrangements  just  indicated 
not  recognized  more  frequently  ? Why  do  even  those 
who  design  costumes  for  the  stage  disregard  them  ? Why 
do  they  not,  through  a little  judicious  deceit,  if  needed, 
in  the  use  of  straight  lines  and  curves,  as  well  as  of  color, 
cultivate  and  satisfy,  with  reference  to  less  favored  forms, 

one’s  sense  of  beauty?  In  fact,  how  can  either  artists  or 
6 


82 


PROPORTION  AND  HARMONY. 


costumers  afford  to  neglect,  as  they  almost  invariably  do, 
their  very  great  opportunities  in  these  directions? 

On  the  principle  that  a half-loaf  is  better  than  none, 
the  mind,  when  these  like  divisions  are  not  revealed  in 

the  arrangements  of  the 
form  as  a whole,  seems  to 
wish  to  see  them  revealed 
in,  at  least,  a part  of  it. 
Thus  the  like  distance  sug- 
gested between  the  top  of 
the  shoe  and  the  upper 
shoe-strings,  and  between 
the  garter  and  the  bottom 
of  the  skirt,  in  the  second 
figure  from  the  left  in  Fig. 
42,  page  81,  does  some- 
thing, though,  of  course, 
very  little,  to  redeem  the 
general  lack  of  propor- 
tional effects  which  the 
other  outlines  manifest. 
So  in  Fig.  71,  page  134, 
the  two  equal  distances 
suggested  between  the 
ankles  and  the  waistband 
of  the  breeches ; and  the 
two,  unequal  to  the  former, 
but  equal  to  each  other, 
between  the  bottom  of 
the  coat  and  the  top  of  the 
head,  and  between  the 
shoulder  and  the  tips  of  the  fingers  of  the  left  hand  ; and 
the  three  equal  distances  in  the  right  arm,  all  afford,  so 


FIQ.  43— A NEW  GUINEA  CHIEF. 
See  pages  83,  130,  131,  132,  133,  141. 


PROPORTION  IN  CLOTHING. 


83 


far  as  they  go,  a certain  degree  of  aesthetic  satisfaction. 
In  Fig.  43,  page  82,  there  is  no  clothing  to  spare.  But 
observe  how  greatly  that  which  accidentally  happens  to 
be  present  enhances  the  artistic  interest.  First  of  all, 
notice  that  the  extremities — by  head-gear,  wristlets,  or 
anklets — are  separated  from  the  rest  of  the  body,  and 
are  not  included  in  the  equal  divisions  suggested  in  it. 
But  aside  from  the  extremities,  the  form  seems  to  be 
equally  divided  above  the  anklets  by  the  bands  about 
the  calves,  by  the  staff,  by  the  girdle,  by  the  ornament  on 
the  breast  in  connection  with  the  bands  about  the  upper 
arms,  and  by  the  band  about  the  neck.  It  is  well  to  ob- 
serve, moreover,  that  the  separation  of  the  extremities, 
necessary  to  the  apparent  division  of  this  figure  into  equal 
parts,  corresponds  to  a method  to  which  we  are  all  more 
or  less  accustomed.  We  cannot  look  at  a boy  in  knicker- 
bockers, for  instance,  without  instinctively  comparing  the 
distance  between  the  tops  of  his  shoes  at  the  ankles  and 
the  bottom  of  his  breeches  with  a like  distance  between 
this  point  and  the  bottom  of  his  jacket.  Nor  can  we  fail  to 
compare  the  length  of  a lady’s  bare  arm  between  the  top  of 
her  glove  and  the  elbow  with  the  length  from  there  to  the 
sleeve.  In  other  words,  as  has  been  said,  when  judging 
of  proportions,  we  instinctively  separate  from  the  form 
the  extremities.  At  the  same  time,  this  does  not  prevent, 
as  shown  on  pages  1 30  and  133,  our  expecting  to  find  ascer- 
tainable ratios  between  the  length  of  the  foot  below  the 
ankle,  or  the  length  of  the  hand  below  the  wrist,  and 
the  measurement  of  the  leg  or  of  the  arm  above  it. 

Even  when  the  whole  form  is  exposed,  it  is  possible,  as 
in  some  of  the  Greek  statues,  to  suggest,  by  surrounding 
arrangements  or  drapery,  these  results  of  like  measure- 
ments. The  Apollo  Belvedere,  for  instance,  Fig.  44, 


84 


PROPORTION  AND  HARMONY. 


page  84,  seems  to  be  divided  according  to  the  very  simple 
ratios  of  I : 2,  1:4,  1 : 8,  2 : 4,  2 : 8,  and  4 : 8.  The  whole 
height  of  the  body  is  apparently  separated,  just  at  the 
broadest  part  of  the  hips,  into  two  parts,  the  half  below  the 
middle  to  be  separated  into  two  parts  at  the  knees,  and 

the  half  above  the  middle  to  be 
separated  into  the  same 
by  the  lower  line  of  the 
scarf  surrounding  the 
neck,  while  the  chin  is 
just  half-way  from  the 
bottom  of  this  scarf  to 
the  top  of  the  head.  The 
trunk  of  the  tree  on 
which  the  right  hand 
leans,  measures,  perpen- 
dicularly, — it  inclines 
somewhat,  — the  same 
as  half  the  height  of  the 
body.  So  does  the  scarf 
from  its  upper  point 
above  the  left  shoulder 
to  its  lower  border.  The 
scarf,  again,  divides  into 
two  equal  parts,  one  ex. 
tending  from  its  ex- 
& v ’ treme  outer  edge  on  the 

right  shoulder  to  its  outer  edge  on  the  left  shoulder,  and 
the  other  from  the  latter  point  to  its  extreme  border  on  the 
left.  Once  more,  the  measurement  from  the  left  side  of 
the  scarf  below  the  left  shoulder  to  the  tips  of  the  fingers 
in  the  right  hand  appears  the  same  as  half  the  height  of  the 
body,  and  near  the  right  elbow  this  last  measurement 
again  is  divided  into  two  equal  parts. 


FIG.  44— THE  APOLLO  BELVEDERE. 


CHAPTER  VII. 


PROPORTIONS  OF  THE  HUMAN  FIGURE  THEORETICALLY 
CONSIDERED. 

Proportion  as  Suggested  by  Imaginary  as  well  as  Real  Lines  Drawn  through 
the  Form — Illustrated  in  the  Case  of  the  Face — Of  other  Parts  of  the 
Body — The  Fact  that  /Esthetic  Judgments  of  the  Form  are  Based 
on  Comparative  Measurements — The  Standards  of  Measurements 
Determined  by  Observation — Observation  of  Nature  Essential  to  Suc- 
cessful Art — Especially  to  Representations  of  the  Human  Form- 
Opportunities  for  Observing  this  in  Greece — Proof  that  the  Excellence 
of  Greek  Sculpture  was  Influenced  by  this  Opportunity— The  Conven- 
tionality of  the  Face  on  Greek  Sculpture  no  Argument  against  this — ■ 
Other  Reasons  why  the  Greek  Face  was  Conventional — The  Greek 
Statues  not  Literal  Imitations — But  their  very  Differences  Show  the  In- 
fluence of  the  Study  of  Nature — Connection  between  Form  and  Signifi- 
cance in  all  the  Arts — Especially  of  those  Representing  the  Human 
Form — 'Physiological  Basis  for  this  View — An  Objection  to  it — Dis- 
guising Concealment  of  the  Form  in  Civilized  Clothing — Disenchanting 
Exposure  of  it  in  Conventional  Art — The  Mean  between  these  Ex- 
tremes— Different  Proportions  as  Appealing  to  Different  Tastes,  and 
as  Vehicles  of  Different  Vibratory  Spiritual  Influences. 


HEN  we  come  to  consider  the  human  body  aside 


from  all  possible  suggestions  afforded  by  the  sur- 
roundings, it  might  be  supposed  that  the  influence  of  such 
lines  as  are  drawn  through  it  or  through  parts  of  it,  in 
Figs.  31,  page  57,  and  32,  page  58,  might  not  be  felt 
because  they  are  not  actually  present.  Nevertheless,  be- 
cause they  are  ideally  present,  they  have  some  influence. 

If,  for  instance,  a person  be  facing  us,  it  is  almost 
impossible  not  to  suppose  an  imaginary  vertical  straight 


86 


PROPORTION  AND  HARMONY. 


line  drawn  from  the  middle  of  his  forehead  to  the  middle 
of  his  chin,  as  in  Fig.  45,  below,  and  if  we  find  this  line 
passing  through  the  middle  of  his  nose,  we  obtain  an  im- 
pression of  regularity  which,  so  far  as  concerns  it  alone,  is 
an  aid  to  the  agreeableness  and  consequent  beauty  of 
the  effect  ; but  in  the  degree  in  which  the  middle  of  the 
nose  is  out  of  this  vertical  line,  not  only  irregularity  but 
ugliness  is  suggested.  A similar  tendency  of  thought 
causes  us  to  suppose  other  imaginary  vertical  straight 
lines,  drawn,  as  in  the  same  Fig.  45,  at  equal  distances 


from  this  central  line  ; and  from  them  we  may  gain  an 
impression  of  relative  regularity  by  noticing  to  what 
extent  the  lines  pass  through  corresponding  sides  of  the 
face.  Besides  this,  we  are  prompted  to  suppose  horizon- 
tal lines  drawn,  as  indicated  in  the  same  figure,  across  the 
forehead,  eyes,  and  mouth  ; and  from  these  lines,  too,  we 
form  judgments  with  reference  to  the  degrees  of  regular- 
ity. If  the  hair  be  farther  down  on  one  side  of  the  fore- 
head than  on  the  other,  or  if  the  arch  of  the  eyebrows 
be  not  symmetrically  rounded,  or  if  the  sides  of  the 


See  pages  15,  59,  86,  87,  105,  120, 
125,  126,  128,  129,  134,  141,  295. 


FIG.  46.— EYE  AND  EAR. 

See  pages  86,  87,  141. 


HUMAN  PROPORTIONS. 


87 


mouth  incline  downward  or  upward,  or  a lip  be  larger  on 
one  side  than  on  the  other,  we  notice  the  fact.  Of  course 
we  do  this,  only  so  far  as  we  compare  the  result  with  that 
of  an  imaginary  straight  line  drawn  through  the  feature. 

The  same  is  true,  too,  with  reference  to  lines  divid- 
ing other  parts  of  the  body.  If  one  part  of  an  eye  or  ear 
(see  Fig.  46,  page  86),  or  if  a neck,  or  hand,  or  trunk, 
or  leg,  be,  relatively  to  other  features  of  the  frame,  too 
long,  or  too  short,  we  perceive  the  defect  almost  imme- 
diately ; but  we  can  only  do  it  as  a result  of  ideally 
drawing  such  lines  as  are  in  Figs.  45  and  46,  and  measur- 
ing and  comparing  the  distances  between  them.  In  the 
same  way,  the  similarity  in  curvature  suggested  by  the 
outer  lines  of  calves,  thighs,  and  shoulders,  prompts  us  to 
imagine  similar  curves  drawn  somewhat  as  in  Figs.  31,  page 
57:  32>  Page  58;  35.  page  70;  36,  page  71;  37,  page 
72  ; 73,  page  137  ; and  74,  page  139,  concerning  which  see 
pages  135  to  138;  and  in  case  there  be  any  deviation 
in  outline  from  conformity  to  a segment  of  one  of  these 
curves,  the  eye  will  observe  the  fact  ; and  the  parts  of  the 
contours  about  which  they  are  described  will  not  seem  to 
be  constructed  on  the  same  lines,  as  we  say,  and,  there- 
fore, will  not  seem  to  be  in  proportion.  So  much  as 
to  the  general  principles  in  accordance  with  which  such 
lines  are  made  the  basis  of  aesthetic  judgments,  either 
because  they  are  actually  delineated  or  are  merely  im- 
agined. 

As  for  the  fact  that  these  aesthetic  judgments  take  place, 
and  that  they  take  place,  as  was  said  on  page  23,  as  a 
result  of  comparing  measurements,  this  is  an  almost  neces- 
sary inference  from  the  phrases  used  by  men  when  speak- 
ing of  the  subject.  Though  willing  to  admit  that  they 
cannot  exactly  define  what  they  mean,  all  are  generally 


88 


PROPORTION  AND  HARMONY. 


ready  to  express  the  opinion  that,  as  compared  with  other 
surrounding  features,  a shoulder,  arm,  nose,  ankle,  foot,  is 
or  is  not  in  proportion,  or  that  the  form,  as  a whole,  is  or 
is  not  well  proportioned.  The  tendency  to  form  such 
judgments,  too,  so  far  as  can  be  ascertained,  has  existed 
from  very  early  times,  influencing  not  only  the  theory  of 
art,  but  also  its  practice.  The  Egyptians  endeavored  to 
embody  their  conceptions  of  the  methods  of  determining 
proportion  by  dividing  the  height  of  the  body  into  fifteen 
equal  sections,  and  the  Greeks,  as  we  shall  find  presently, 
into  six  or  eight. 

Before  deciding  which,  if  any,  of  these  methods  is  pre- 
ferable, let  us  begin  by  asking,  first,  how  we  are  to  come 
to  a decision.  The  answer,  of  course,  is  by  making  a 
study  of  the  human  form.  But  how  shall  we  make  this 
study?  In  our  own  day,  no  one  would  concede  that  this 
could  be  done  except  through  some  method  founded  upon 
observation.  Readers  of  this  book  have  probably  had 
their  attention  drawn  to  the  measurements  published  by 
D.  A.  Sargent,  M.D.,  of  Harvard  College,  in  his  articles 
entitled  “ The  Proportions  of  the  Typical  Man,”  “ Physical 
Characteristics  of  the  Athlete,”  and  “ Physical  Develop- 
ment of  Woman,”  published  in  “Scribner's  Magazine,”  of 
the  dates,  respectively,  of  July,  1887,  November,  1887,  and 
February,  1889.  These  measurements  were  the  results  of 
the  examination  of  large  numbers  of  subjects,  many  of 
whom,  by  their  success  in  wrestling,  running,  ball-playing, 
and  other  gymnastic  work,  had  shown  certain  parts  of 
their  bodies  to  be  well  developed  ; and  the  articles  furnish, 
for  estimating  the  proportions  of  the  typical  man,  one 
method,  at  least,  thoroughly  scientific.  In  connection 
with  this,  to  many  parts  of  the  body  thus  tested  the 
methods  of  composite  photography  may  now  be  applied. 


HUMAN  PROPORTIONS. 


89 


Indeed,  there  is  no  reason  why  standards  for  the  guidance 
of  artists  should  not  be  furnished  in  our  age  far  more 
scientific  than  any  that  were  ever  before  conceived. 

It  must  not  be  supposed,  however,  that  the  general 
recognition  of  the  necessity  of  observation  is,  in  any  sense, 
peculiar  to  modern  times.  Though  induction,  as  a philo- 
sophic method,  was  not  formulated  till  the  time  of  Bacon, 
it  has  been  practised  ever  since  the  origin  of  the  human 
mind  ; and  in  every  period  of  high  attainment  it  has  been 
practised  extensively.  Nor  does  the  history  of  art  furnish 
any  exception  to  this  statement,  though,  at  many  different 
periods,  certain  works  have  been  produced  in  large  num- 
bers on  the  supposition  that  mere  theories  of  form,  origi- 
nally derived,  of  course,  from  nature,  but  finally  held 
independently  of  it,  could  be  substituted  for  continued 
and  careful  observation.  We  find  such  works  among  the 
remains  of  the  arts  of  Egypt  and  Assyria,  as  well  as  of 
Greece  prior  to  the  time  of  Daedalus.  We  find  them  in 
the  painting  and  sculpture  of  the  primitive  Christians,  and 
of  the  Middle  Ages.  We  find  them  in  the  conventional 
flowers  and  leaves  wrought  into  the  decorations  of  the 
earlier  Gothic  cathedrals.  We  find  them  in  many  of  the 
figures  and  landscapes  of  the  arts  of  China  and  Japan; 
and  we  find  them  in  designs  for  illustrations  of  books 
and  for  ornamentations  on  walls,  even  in  elaborately 
wrought  products  of  the  decorative  and  what  is  termed 
the  decadent  art  of  our  own  day;  but  we  find  them  in 
the  foremost  products  of  no  age  or  style  in  which  art  is 
acknowledged  to  have  been  at  its  best. 

What  is  true  of  the  representation  of  other  appearances 
in  the  world  about  us,  is  true  of  that  of  the  human  figure. 
It  is  as  impossible  to  produce  successful  pictures  or  statues 
of  any  kind  without  studying,  at  every  stage,  the  forms 


90 


PROPORTION  AND  HARMONY. 


of  visible  nature,  as  to  produce  successful  poems  without 
studying,  at  every  stage,  the  forms  of  audible  speech. 
Those  who  imagine  that  by  looking  elsewhere  than  to 
nature  they  can  find  guidance  which  is  a substitute  for 
it,  have  not  read  aright  the  history  of  art,  and  do  not 
understand  the  character  of  its  mission. 

If,  with  this  thought  in  mind,  we  look  farther  into  the 
subject,  we  shall  find  that  never — except,  perhaps,  in  Japan 
— among  a people  sufficiently  cultivated  to  avail  them- 
selves of  their  aesthetic  advantages,  have  such  opportuni- 
ties been  afforded  for  observing  the  human  form  under 
the  best  conditions,  whether  at  rest  or  in  motion,  as 
among  the  ancient  Greeks.  Owing  to  the  peculiar  nature 
of  their  social,  civil,  and  religious  habits  and  observ- 
ances, they  became  accustomed,  as  an  every-day  occur- 
rence, to  gaze  upon  this  form  in  a state  but  slightly 
removed  from  that  of  nature.  The  artist  of  the  present 
is  obliged  to  make  his  observations  upon  a small  number 
who  follow  the  profession  of  posing  in  the  presence  of 
painters  and  sculptors  only,  and,  of  course,  with  all  the  self- 
consciousness  that  their  employment  involves.  The  artist 
of  Athens  could  choose  from  thousands  moving  about 
him  in  the  freedom  of  nature,  giving  unconscious  and  un- 
constrained expression  to  every  motive,  and  besides  this, 
he  could  have  his  own  judgments  confirmed  by  the  ver- 
dicts of  an  entire  populace,  one  of  whose  chief  delights 
consisted  in  criticising  and  comparing  the  curve  of  every 
limb,  and  the  grace  of  every  movement  that  was  supposed 
to  render  one  of  the  favorites  of  the  city  more  beautiful 
or  attractive  than  another. 

It  is  such  facts  as  these  that  warrant  the  attention 
that,  in  modern  times,  has  been  given  to  Greek  sculpture. 
Naturally,  too,  the  excellence  of  this  sculpture,  taken  in 


GREEK  CONCEPTION  OF  NEMAN  FORM. 


91 


connection  with  the  testimony  of  Greek  and  Roman 
writers,  has  given  rise  to  the  opinion  that  the  result  was 
largely  due  to  a study  of  proportion  in  the  abstract.  But 
notice  that  even  this  study  need  not  involve  neglect  of  the 
study  of  nature  in  the  concrete.  The  human  mind  being 
what  it  is,  it  is  more  than  likely  that  the  Greek  in  his 
circumstances  would  have  used  models  even  more  exten- 
sively than  is  done  to-day  ; and,  not  only  so,  but  also,  on  ac- 
count of  his  greater  opportunities  for  observation,  that  he 
would  have  used  them  more  judiciously.  What  if  he  did 
form  certain  theories  concerning  proportion?  Are  there 
any  thinking  minds,  or  many,  that  can  practise  any  pro- 
fession for  any  length  of  time,  without  developing  theo- 
ries concerning  it  ? The  fact  that  the  Greeks  had  these 
does  not  involve  their  being  servile  imitators  of  one  an- 
other’s works,  or  even  believers  in  one  another’s  concep- 
tions. The  painter  Eupompus  told  the  sculptor  Lysippus 
(Pliny’s  Nat.  Hist.,  xxxiv,  19)  that  “ Nature  herself  is  to  be 
imitated,  not  the  artist,” — which  opinion  possibly  underlay 
that  development  of  the  art  in  the  hands  of  the  latter  to 
which  Pliny  refers  when  he  says:  “He  added  much  to 
statuary  by  making  the  heads  smaller  and  the  bodies  more 
graceful  and  less  bloated  ; through  which  the  height  of  stat- 
ues seemed  greater.”  “ ‘ That  you,  Cleito,’”  said  Socrates, 
according  to  the  “ Memorabilia,”  iii,  10,  6,  “ ‘ make  different 
forms,  racers,  wrestlers,  boxers,  and  experts  in  all  kinds  of 
gymnastics,  I see  and  understand ; but  if  you  wished  to 
bring  out  the  soul  of  man  through  the  form  so  that  it 
should  appear  a living  thing,  how  would  you  work  this  into 
a statue?’  When  Cleito,  looking  away,  was  slow  in  an- 
swering, ‘ Would  you  not,’  continued  Socrates,  ‘ make 
your  work  a copy  of  the  appearances  of  living  men  ? ’ 
‘ Certainly  so,’  ” was  the  reply.  And  in  a country  in 


92 


PROPORTION  AND  HARMONY. 


which  the  artist  had  such  opportunities  of  studying  the 
appearances  of  living  men,  we  can  scarcely  imagine  how 
Cleito  could  have  given  a different 
answer.  What  need  would  he  have 
to  fall  back  upon  other  artists’  pro- 
ducts or  theories?  Interested,  as  he 
would  necessarily  be,  in  the  personal 
charms  of  those  about  him,  would 
it  not  be  unnatural  for  him  to  do 
otherwise  than  reproduce  them  as 
they  were?  Like  Raphael,  Titian, 
Shakespeare,  Goethe,  and  innumer- 
able artists  since  his  time,  would  he 
not  care  as  much,  at  least,  for  hu- 
manity as  for  mathematics?  But 
why  need  one  ask  these  questions? 
What  were  the  masterpieces  of  the 
painter  Apelles  and  of  the  sculptor 
Praxiteles?  The  first  is  said  to 
have  been  the  “ Venus  Anadyo- 
merne;  ” the  second  the  original  of 
the  Venus  de’  Medici  (Fig.  47)  ; and 
both  are  said  to  have  been  modelled 
after  the  form  of  the  Athenian  beau- 
ty, Phryne  (Pliny’s  Nat.  Hist.,  xxxv, 
36,  note  59;  xxxiv,  19,  note  43.) 

One  fact  always  affords  a strong 
argument  in  support  of  the  theory 
that  Greek  sculpture  was  produced 
mainly  by  an  application  of  math- 
ematical principles,  and  this  is  the  conventional  character 
of  the  face  of  the  statue.  With  few  exceptions,  the  nose, 
mouth,  eyes,  and  forehead  all  show  the  results  of  the  same 


FIG.  47— VENUS  DE’  MEDICI. 
See  pages  92, 97, 99, 102, 141. 


GREEK  CONCEPTION  OF  HUMAN  FORM. 


93 


relative  measurements;  and  the  question  is  asked  very  pert- 
inently, If  the  face  were  conventional,  why  was  not  the  form 
also  ? To  answer  this  question,  makes  it  necessary  to  direct 
attention  to  something  which  we  moderns  find  it  difficult 
to  understand,  yet  which  nevertheless  seems  to  be  a fact, 
namely,  that  the  impression,  or  expression,  of  beauty  on 
the  part  of  the  human  figure,  in  the  conception  of  the 
Greek,  had  comparatively  little  to  do  with  the  face.  Any 
one  who  has  ever  stood,  as  has  the  writer,  in  a narrow 
street  in  Constantinople,  and,  at  the  risk  of  offending  the 
authorities,  gazed  critically  at  the  ladies  of  the  Sultan’s 
harem,  when,  under  the  protection  of  their  eunuchs,  half 
a hundred  of  them,  perhaps,  were  being  driven  past  in 
their  carriages,  all  forms  and  faces  being  concealed  with 
the  exception  of  the  eyes,  has  probably  been  made  to 
realize,  as  never  before,  how  much  expression  there  is  in 
the  eyes.  From  these  alone,  one  is  able  to  form  a judg- 
ment, though,  of  course,  very  superficial,  of  the  general 
characteristics  of  their  owners.  If  an  ancient  Greek  were 
to  be  raised  to  life  in  our  day  and  country,  he  would  see, 
in  some  cases,  human  beings  with  every  part  of  their 
forms  concealed  except  their  hands  and  faces.  This 
would  be  a new  experience  to  him,  and  it  probably  would 
be  accompanied  by  a discovery  with  reference  to  the 
capabilities  of  expression  in  the  human  countenance  both 
as  regards  thought  and  character,  of  which  he  never 
before  had  conceived.  The  fact  is,  that  character  and 
thought  are  expressed  in  the  whole  human  figure.  Of 
this,  the  face  forms  a very  small  part.  If  we  are  in  cir- 
cumstances where  we  can  see  the  whole  figure,  there,  by  a 
necessary  law  of  the  mind,  we  think  mainly  of  that  which 
occupies  the  main  part  of  the  field  of  vision.  If  we  have 
analyzed  our  own  thoughts,  when  witnessing  a scene  in 


94 


PROPORTION  AND  HARMONY. 


which  the  clothing  of  the  performers  was  less  ample  than 
that  allotted  by  our  standards  of  civilization, — an  athletic 
exhibition,  or  the  bathing  of  boys  on  the  seashore, — we 
shall  recall  that  those  with  the  finest  forms  and  most 

graceful  movements  invari- 
ably attracted  our  attention 
and  won  our  admiration,  no 
matter  how  ugly  may  have 
been  their  countenances. 
In  such  circumstances,  we 
scarcely  seem  to  notice 
countenances  at  all.  This 
was  the  condition  and  atti- 
tude of  the  Greek.  And  the 
fact  in  his  case,  and  the  rea- 
son for  it,  seem  to  furnish  a 
satisfactory  answer  to  the 
theories  of  some  modern 
artists  and  critics  who  hold 
that  because,  in  Greek  art, 
the  face,  as  a rule,  is  com- 
paratively expressionless,  it 
should  be  so  in  modern  art. 
Here  is  one  of  those  abund- 
ant instances  in  which  cir- 
cumstances alter  cases.  One 
reason  why  Greek  art  was 
great  is  because  it  was 
true  to  Greek  life.  Mod- 
ern art  can  become  great  only  in  the  degree  in  which  it  is 
true  to  modern  life. 

But  now  for  our  main  application  of  what  has  been 
said.  Many  beautiful  forms  that  served  as  models  for  the 


FIG.48.— FARNESE  HERCULES,  BY  GLYCON 
THE  ATHENIAN. 


See  page  97. 


GREEK  CONCEPTION  OF  HUMAN  FORM. 


Greek  artists  were  un- 
doubtedly surmounted 
by  ugly  faces.  The 
Greek  did  not  believe 
in  ugliness  anywhere ; 
and  for  this  reason,  i 
place  of  the  faces  that 
he  found,  he  may 
substituted  his  con- 
ventional face,  prob- 
bly  itself  a copy  of 
some  face  which  com- 
mon opinion  had  pro- 
nounced beautiful. 

Moreover,  by  using 
this  face  and  no  other, 
he  would  avoid  giving 
offence  to  those  who 
might  desire  to  have 
him  reproduce  their 
countenances  as  well 
as  forms.  Besides  this, 
too,  large  numbers  of 
his  statues  represented 
gods,  and  it  would 
scarcely  have  been  con- 
sidered appropriate 
had  he  represented 
these  by  using  a lit- 
eral portrait  of  a living 
person. 

Once  more,  it  must  fig.  49.— diadumenos,  by  polycleitus. 
not  be  supposed,  even  See  pages  97,  132,  141. 


96 


PROPORTION  AND  HARMONY. 


though  it  be  admitted  that  the  Greek  used  models  freely, 
that  he  was  often  content  to  have  all  the  parts  of  any  one 
statue  literally  reproduce  all  the  parts  of  any  one  model. 


FIG.  50.— THE  DISCOBOLUS,  OR  QUOIT-THROWER. 
See  pages  97,  141. 


On  the  contrary,  the  history  of  the  best  period  of  his  art  is 
a record  of  changes  in  forms,  as  these  were  developed  with 
more  or  less  gradualness,  the  one  from  the  other.  The 
earliest  style  is  termed  muscular  and  bold,  as  exemplified 
in  the  lost  wooden  statue  of  Hercules  by  the  prehistoric 


GREEK  CONCEPTION  OF  HUMAN  FORM. 


97 


Daedalus.  The  Farnese  Hercules,  Fig.  48,  page  94,  by 
Glycon,  an  Athenian  sculptor  supposed  to  be  of  the 
time  of  Hadrian,  born  A.D.  76,  is  said  to  represent  the 
characteristics  of  this  Hercules,  as  copied  previously  by 
the  portrait-sculptor  Ly- 
sippus about  372-316  B.C. 

Next  we  have  the  “ athlet- 
ic ” style  of  Ageladas  pre- 
ceding 500  B.C.,  of  which 
we  still  have  representa- 
tions in  the  works  of  his 
pupils, — the  Diadumenos 
(Fig.  49,  page  95)  of  Poly- 
cleitus,born  about  482  B.C., 
and  the  Discobolus(Fig.  50, 
page  96)  of  Myron,  born 
about  500  B.C.  Developed 
at  the  same  time,  but  usual- 
ly described  as  a little  later, 
by  another  pupil  of  Agel- 
adas, we  have  the  more 
refined  “ grand  ” style  of 
Pheidias,  born  about  500 
B.C.,  and  exemplified  in  his 
Minerva  and  Jove  and  oth- 
er compositions  connected 
with  the  Parthenon.  The  statue  in  Fig.  51,  is  supposed  by 
some  to  be  a literal  copy  of  the  Minerva  of  Pheidias, 
and  the  Theseus,  Fig.  52,  page  98,  is  itself  one  of  the 
statues  of  his  Parthenon.  Then  we  have  the  delicate 
and  “ graceful  ” style  of  Praxiteles,  a pupil  of  Phei- 
dias, illustrated  in  the  Faun  (Fig.  53,  page  99),  the 
Venus  (Fig.  47,  page  92),  and  the  Hermes  (Fig.  54,  page 
7 


FIG.  51.— PALLAS  OF  VELLETRI. 
LOUVRE,  PARIS. 

See  page  97. 


98 


PROPORTION  AND  HARMONY. 


ioo).  About  the  same  time  as  the  “ graceful  ” style,  there 
is  said  to  have  been  developed  the  “ historical  ” style  of 
the  portrait-sculptor  Lysippus ; and  the  “ impassioned  ” 
style,  still  preserved  to  us  in  the  group  of  Niobe  and  her 
children  (Fig.  55,  page  101),  supposed  to  be  the  work  of 
Scopas,  and,  a little  later,  in  the  Laocoon  and  other  statues 


of  the  Rhodian  School.  Finally  we  hear  of  the  “ colossal  ” 
style,  in  which  Chares,  a pupil  of  Lysippus,  executed  the 
Colossus  of  Rhodes.  But  notwithstanding  the  general 
fact  that  these  styles  were  developed  one  after  another, 
it  is  also  true  that  many  of  them  were  developed  at  the 
same  period.  For  instance,  the  Apollo  Belvedere,  Fig. 
44,  page  84,  supposed  to  be  a copy  of  an  original  by 
Praxiteles,  is  as  nearly  allied  to  the  “ grand  ” style  as  to 


GREEK  CONCEPTION  OF  HUMAN  FORM. 


99 


the  “ graceful,”  of  which  that  sculptor  is  supposed  to  be 
the  chief  master.  Notice, 
too,  the  very  great  differ- 
ences in  form  perceptible 
between  Figs.  44,  page  84; 

56,  page  102  ; and  58,  page 
104;  also  between  Figs.  47, 
page  92,  and  59,  page  105  ; 
and  also  between  Fig.  53, 
and  Figs.  54,  page  100,  and 
58,  page  104, — all  supposed 
to  be  copies  of  statues  pro- 
duced at  about  the  same 
period.  In  the  “graceful” 
style,  moreover,  measure- 
ments which  in  former 
periods  were  applied  exclu- 
sively to  the  male  figure 
alone, orto  the  femalealone, 
came  to  be  applied  to  both 
conjointly.  (Notice  again 
this  Fig.  53,  and  Fig.  57,  page 
103.)  Would  this  ever  have 
been  done,  or  even  thought 
of,  except  by  artists  accus- 
tomed to  unite  in  the  same 
form  characteristics  of  dif- 
ferent living  models?  We 
are  told  that,  when  the  Hol- 
land-English  sculptor  Ruys- 
brack  was  preparing  his 
Hercules,  he  took  for  the  head  of  the  statue  the  con- 
ventional head  of  the  Greek  god,  but  for  the  rest  of  the 


FIG.  53.— THE  FAUN  OF  PRAXITELES. 

See  pages  97,  99,  141. 


FIG.  54.— HERMES  OF  PRAXITELE8. 

ioo  See  pages  97,  99,  102,  132,  141. 


GREEK  CONCEPTION  OF  HUMAN  FORM. 


IOI 


body  various  parts  of  the  forms  of  some  half-dozen  of  the 
best  gymnasts  of  London.  The  painter  Ellis,  for  instance, 
sat  for  the  legs.  There  are  reasons  for  supposing  that  cer- 
tain of  the  methods  of  the  ancients  did  not  differ  essentially 
from  this.  They  used  models,  but  probably  rejected  the 
members  of  a model  that  did  not  conform  to  accepted 
standards. 


FIQ.  55— FROM  GROUP  OF  NIOBE  AT  FLORENCE. 

See  pages  59,  98. 

Suggested  by  the  thought  in  the  last  paragraph,  there 
is  another  consideration  which,  in  studying  the  proportions 
of  the  human  body,  necessitates  taking  the  observation  of 
nature  for  the  point  of  departure.  This  is  the  fact  that 
different  forms  of  men,  even  when  conforming  to  accepted 
standards,  or  conforming  sufficiently  to  be  all  equally  well 
proportioned,  differ  in  their  measurements.  Among  the 
Greek  statues,  for  example,  the  athletes,  as  contrasted 
with  other  men,  have  broader  measurements  at  the 


102 


PROPORTION  AND  HARMONY. 


shoulders,  as  seen  both  from  the  front  and  the  sides,  and 
their  whole  forms  taper  more  decidedly  between  the 
shoulders  and  the  ankles  ; the  children  have  comparatively 
larger  heads,  longer  trunks,  shorter  limbs,  and  smaller 

feet ; while,  as  contrast- 
ed with  the  men,  most 
of  the  women,  but  not 
all,  have  a height  about 
one  tenth  less,  and  eight 
times,  instead  of  six 
times,  the  length  of  the 
foot,  and  have  shoul- 
ders relatively  narrower, 
thighs  broader,  and  all 
outlines,  including  limbs, 
hands,  fingers,  and  nails, 
more  perfectly  tapered 
and  rounded.  Compare 
Figs.  44,  page  84,  and  54, 
page  100,  with  47,  page 
92,  and  59,  page  105. 
As  shown,  too,  in  Chap- 
ter VII.  of  “ Painting, 
Sculpture,  and  Archi- 
tecture as  Representa- 
tive Arts,  ” such  varia- 
tions may  be  ascribable 
to  differences  not  only 
in  occupation,  age,  and 
sex,  but  also  in  temperament, — the  mental,  the  vital,  and 
the  motive,  which  are  respectively  expressive  of  very 
different  intellectual  and  physical  traits,  each  tending  to 
a different  general  contour. 


FIG.  56.— MELEAQROS,  IN  THE  VATICAN. 
See  pages  99,  141. 


FIG.  57.— GANYMEDE,  AFTER  LEOCHARES,  IN  THE  VATICAN. 
See  pages  gg,  132,  141. 


103 


104 


PROPORTION  AND  HARMONY. 


This  connection  between  the  contour  and  the  traits 
represented  by  it  merely  carries  out  an  analogy  which  is 

true  in  every  form  of  art. 
A man,  in  writing  a song 
or  a poem — -whether  a 
drama  or  a lyric — must 
begin  by  making  it  fulfil 
the  requirements  of  con- 
gmity  (see  “ The  Genesis 
of  Art-Form,”  Chapter 
IX.);  i.  e.,  by  making  it 
conform  strictly  to  a man’s 
natural  mode  of  express- 
ing the  emotion  or  con- 
ception intended  to  be 
conveyed.  Otherwise,  all 
that  is  excellent  in  the 
poem  will  be  virtually 
wasted.  So  of  all  that  is 
excellent  in  a painting  or 
a statue  in  the  way  of  pro- 
portion. Especially  is 
this  true,  as  related  to  the 
human  form.  One  must 
always  bear  in  mind  that 
its  proportions  are  express- 
ive of  significance.  All 
the  members,  whether 
connected  with  forehead, 
eyes,  ears,  nose,  mouth, 
chin,  neck,  shoulders, 
arms,  hands,  waist,  hips,  legs,  calves,  ankles,  feet,  are 
adapted  to  some  purpose  ; in  our  minds  they  are  associated 


FIG.  58.— APOLLO  SAUROCTONOS— 
PRAXITELES— VATICAN. 

See  pages  99,  141. 


H UMA  N PROP  OR  TIONS  RELA  TIVE  TO  CHAR  A CTER  1 05 


with  this  purpose  ; and  seem  beautiful  or  ugly,  on  account, 
partly,  of  the  way  in  which  they 
fulfil  it,  and,  partly,  of  the  de- 
ficiency or  superabundance  of 
the  characteristics  supposed 
to  be  represented  by  them,  in 
case  they  are  relatively  smaller 
or  larger  than  is  usual.  This 
is  true  as  applied  to  combina- 
tions, the  beauty  of  which  is 
ordinarily  judged  to  be  depend- 
ent upon  form  solely.  For 
instance,  take  those  outlines 
in  the  countenance  composing 
what  are  ordinarily  described 
as  regular  features.  When,  as 
in  these,  after  drawing  verti- 
cal and  horizontal  lines  across 
the  face  (see  Fig.  45,  page  86), 
the  corresponding  parts  of  eye- 
brows, eyes,  nostrils,  on  the  op- 
posite sides  of  the  face,  appear 
to  be  in  exact  balance,  inas- 
much as  the  whole  is  outlined 
by  a framework  that  is  exact- 
ly square  or  rectangular,  the 
external  arrangement  is  satis- 
factory because  it  seems  repre- 
sentative of  something  internal 
that  is  satisfactory ; in  other 
words,  because  we  associate 
these  physical  conditions  with 
correlated  ones  that  are  mental 


FIQ.  59.— VENUS  ASCRIBED  TO 
STYLE  OF  PRAXITELES. 


See  pages  99,  102,  141. 

and  moral.  Because 


io6 


PROPORTION  AND  HARMONY. 


the  face  is  square,  we  judge  that  the  character  is  square. 
For  instance,  Mephistopheles  as  represented  on  the  stage 
is  always  painted  with  the  arch  of  the  eyebrows  not  in 
line  with  the  horizontal,  but  beginning 
high  up  on  the  temples  and  running 
downward  toward  the  bridge  of  the 
nose  (see  Fig.  60).  This  is  the  way, 
too,  in  which  even  a handsome  man 
looks  when  contracting  his  brows 
under  the  influence  of  arrogance,  pride, 
contempt,  hatred,  and,  most  of  all, 
of  malice  (see  Fig.  61).  With  a sim- 
ilar general  effect  of  irregularity,  a 
simpleton  on  the  stage  is  painted  with 
nostrils  and  lips  which  exaggerate 
the  expression  of  the  smile  by  run- 
ning too  far  up  at  the  sides  ; and  a scold,  with  the  sides 
of  the  same  features  exaggerating  the  expression  of  the 
sneer  and  frown,  by  running  too  far 
down.  Or  if  we  consider  combinations 
which  almost  every  one  admires,  of  a 
comparatively  small  ankle  and  large 
calf,  or  of  a small  wrist  and  large  fore- 
arm, or  of  a small  waist  and  broad 
shoulders,  or,  in  a woman,  broad  hips; 
certainly  one  way  of  explaining  the 
effects  of  combinations  of  this  kind  is  to 
attribute  them  to  significance.  Clumsy  fig.  6i. 

joints  at  the  places  where  the  body C0NTEMPT  AND  anger. 
must  bend  suggest  a lack  of  flexibility,  See  PaRe  Io6- 
deftness,  and  grace  ; and  slender  muscles  at  the  places 
where  the  body  must  exert  itself  suggest  a lack  of  stabil- 
ity, strength,  and  persistence.  Therefore,  though  the  curve 


FIG.  60. 

MEPHISTOPHELES. 

See  page  106 


HUMAN  PROPORTIONS  RELATIVE  TO  CHARACTER.  IO  7 

connecting  the  ankle  with  the  calf,  or  the  wrist  with  the 
forearm,  or  the  waist  with  the  breast  or  hips,  is  beau- 
tiful, as  will  be  shown  by-and-by,  because  it  fulfils  a re- 
quirement connecting  together  with  ease  two  outlines  in 
vision,  it  is  beautiful  also  because  it  fulfils  a requirement 
connecting  together  with  satisfaction  two  facts  in  thought. 
After  all  that  can  be  claimed,  therefore,  for  the  effects  of 
mere  outlines,  there  remain  certain  other  requisites  of 
beauty  for  which  these  never  can  account.  They  can  be 
attributed  to  significance  alone,  under  which  general  term 
we  may  include,  for  reasons  given  in  Chapter  XV.  of 
“ Art  in  Theory,”  all  such  suggestions  as  are  contained  in 
conceptions  like  those  of  adaptability,  fitness,  association, 
symbolism,  sympathy,  and  personality. 

Indeed,  even  upon  the  supposition  that  beauty  is 
merely  a physiological  effect  of  form,  this  conclusion  is 
inevitable.  As  will  be  brought  out  in  Chapter  XX.  of  this 
volume,  the  most  subtle  conceivable  effects  of  harmony, 
whether  of  sound  or  color,  are  results  of  experiencing  a 
regularly  recurring  series  of  vibrations  causing  the  nerves 
to  thrill  or  glow  ; whereas  effects  of  discord  are  results  of 
irregularly  recurring  series  of  vibrations  causing  a sensa- 
tion of  a jar  or  shock.  But  whence  comes  the  thrill  or 
the  shock,  as  the  case  may  be  ? Every  physiologist  ad- 
mits that  the  nerves  may  be  affected  not  only  from  the 
sense-side,  but  also  from  the  mind-side.  A man  suffers  in 
spirits  and  health  not  only  because  of  influence  exerted 
upon  his  body  from  without,  but  also  because  of  influence 
coming  from  his  own  thoughts  and  emotions.  It  is  a 
simple  physiological  fact,  therefore,  that,  even  though  the 
nerves  may  be  agreeably  affected  by  a form,  nevertheless 
if,  owing  to  a lack  of  adaptability  or  fitness,  or  to  a fail- 
ure to  meet  the  mind’s  requirements  of  association,  sym- 


io8 


PROPORTION  AND  HARMONY. 


holism,  sympathy,  or  personality,  certain  suggestions  of 
the  form  jar  upon  one’s  sense  of  congruity  or  propriety, 
or,  as  we  say,  shock  one’s  sensibilities,  then  even  the  phys- 
iological condition  which  is  the  subjective  realization  of 
the  presence  of  beauty  will  not  ensue. 

The  author  is  aware  that  to  take  this  ground  is  to  meet 
with  the  accusation,  on  account  of  the  one  subject  to 
which  the  principle  is  most  frequently  applied,  that  he  is 
confounding  the  aesthetical  with  the  ethical.  But  this 
is  not  so.  It  seems  so  because  the  dictates  of  conscience 
are  more  apt  to  be  the  same  in  all  men  than  those  of 
any  other  part  of  one’s  nature,  and  because,  therefore,  that 
which  violates  these  dictates  is  that  which  is  most  likely 
to  appear  distasteful  to  the  largest  number.  But  the 
principle  involved  applies  to  a vast  range  of  subjects 
which  have  nothing  to  do  with  ethics.  A picture  untrue 
to  the  requirements  of  history  also,  or  to  the  scenes  of  a 
locality,  might  have  a correspondingly  distasteful  effect 
upon  the  mind  of  an  historian  or  a traveller;  might  so  jar 
upon  his  sensibilities  as  to  counterbalance  entirely  any 
possible  degree  of  excellence  in  form  considered  merely 
as  form. 

As  applied  to  the  human  figure,  and  to  the  expression, 
through  every  part  of  it,  of  a particular  phase  of  signifi- 
cance, it  is  apparent  that  certain  legitimate  deductions 
from  this  principle  are  often  ignored.  When  this  is  said, 
it  must  be  said  also,  if  we  are  to  deal  with  the  subject 
with  perfect  truth,  that  they  are  ignored  almost  as  much 
in  certain  disguising  concealments  of  the  form  character- 
izing some  of  the  customs  of  civilization,  as  in  certain 
disenchanting  exposures  of  it  characterizing  some  of  the 
conventionalities  of  art.  Viewing  the  subject  not  with 
the  prejudice  which  supposes  that  whatever  is,  is  neces- 


CLOTHING  AND  SIGNIFICANCE. 


IO9 


sarily  right,  and  therefore  finds  fault  with  straight  skirts 
on  a woman  merely  because  others  are  wearing  hoops, 
and  with  knickerbockers  on  a man  merely  because  others 
are  wearing  pantaloons;  but  viewing  the  subject  in  a 
rational  way,  it  may  be  said  that  the  human  form  just  as 
it  is,  is  God-made,  whereas  human  clothing  is  man-made; 
and  that  the  latter,  even  though  it  drag  for  yards  behind 
the  feet,  especially  if  with  just  enough  exposure  to  sug- 
gest a possibility  of  more  exposure,  may  be  in  its  tend- 
ency less  humanizing,  in  a good  sense,  than  a garb 
disclosing  enough,  at  least,  to  allow  free  and  natural 
expression  to  the  soul  within.  The  Hebrew  priest 1 was 
told  to  sprinkle  the  blood  of  a sacrificial  victim — represent- 
ing life  that  was  innocent  and  therefore  spiritual — on  the 
vessels  of  the  temple  every  time  that  he  had  occasion  to 
use  them.  The  people  were  thus  taught  that  nothing  in 
the  world  that  is  material,  not  even  a consecrated  imple- 
ment of  the  sanctuary,  is  sacred  except  when  made  to 
represent  the  presence  of  spiritual  life.  Much  less  is  the 
material  clothing  of  human  figures  sacred.  One  might 
argue  that  it  can  never  represent  spiritual  life  quite  as 
well  as  when  it  faithfully  reveals  the  general  outlines  of 
the  form  which  the  creative  power  designed  that  spiritual 
life  on  earth  should  have.  Or — to  examine  the  subject 
in  the  light  of  its  practical  effects — what  artist  ever  repre- 
sented a wanton  in  the  scanty  short  skirts  and  bare  feet 
of  a peasant  ? What  man,  so  far  as  form  in  dress  could 
affect  him,  would  not  be  conscious  of  more  kindly,  tender, 
generous,  and  protective  impulses  awakened  in  him  by  the 
simple  clothing  of  the  latter,  or  of  a young  girl  just  enter- 
ing her  teens,  than  by  the  trailing  silks  and  laces  of  the 

1 Ex.  29  : 20,  21  ; Lev.  1:5,  11  ; 3:2,  8,  13  ; 7 : 2 ; 17  : 6,  ri  ; Num. 
18  : 17  ; 19  : 4. 


I IO 


PROPORTION  AND  HARMONY. 


former  ? Thus  much  for  one  of  the  many  mistakes  of 
civilization.  No  influence  is  more  indirectly  exalting  than 
beauty,  and  no  beauty  ought  to  be  more  exalting  than 
that  of  the  human  form.  To  veil  it  wholly,  as  the 
oriental  women  do  their  faces,  may  impair  the  charm  of 
life  not  only,  but  its  chastity.  When  much  that  is  con- 
cealed, might  if  revealed,  put  an  end  both  to  legitimate 
curiosity  and  to  purely  aesthetic  desires,  might  it  not  also 
put  an  end  to  much  that,  when  developed,  reinforces 
desires  of  a less  exalted  nature  ? It  is  certainly  a ques- 
tion whether,  in  such  cases,  complete  satisfaction  would 
not  often  accompany  that  which  satisfied  merely  the  eye. 
The  Japanese,  familiar  from  childhood  with  an  almost 
total  exposure  of  the  form,  and  notwithstanding  tra- 
ditionally low  standards  of  conventional  morality,  are 
believed  by  themselves,  and  by  others  who  have  studied 
them,  to  be,  absolutely  considered,  more  moral  by  nature, 
in  that  they  are  less  prone  to  morbid  and  soulless  forms 
of  indulgence,  than  are  the  Europeans.  Is  not  one  proof 
of  this — as  it  certainly  is  a proof  of  the  delicacy  of  their 
sense  of  propriety  and,  for  that  matter,  of  beauty- 
afforded  by  the  fact  that,  in  their  higher  art,  complete 
nudity  is  never  depicted? 

So  much  for  a mistake  of  conventional  fashion.  Now 
a few  words  with  reference  to  a mistake  in  an  opposite 
direction  made  by  conventional  art.  The  true  principle 
in  art  is  that  it  should  represent  life,  and,  if  dealing  with 
human  life,  should  represent  that  which  is  in  the  highest 
sense  humanizing.  But  that  which  is  in  the  highest 
sense  humanizing  gives  principality  to  mental  and  spirit- 
ual suggestions,  and  keeps  others  subordinate.  Can  this 
be  said  to  be  done  when  parts  of  the  body,  which  even  bar- 
barians conceal,  are  exposed,  in  conditions,  as  sometimes 


CLOTHING  AND  SIGNIFICANCE. 


Ill 


happens  in  modern  art,  so  different  from  those  of  nat- 
ural life  that  one  is  forced  to  the  inference  that  they  are 
exposed  for  the  sole  purpose  of  exposure?  In  answer 
to  this  we  are  referred  to  Greek  art.  But  Greek  art  was 
true  to  the  conditions  of  Greek  life.  The  legitimate 
deduction  is  that  our  art  should  be  true  to  the  conditions 
of  our  life.  Then  again  we  are  referred  to  the  use  of 
models  by  our  artists  ; and  this  is  the  sort  of  argument 
that  makes  a sensible  man  feel  faint.  A gentleman  uses  a 
dressing-room.  To  prove  himself  a gentleman  need  he  in- 
vite the  public  to  witness  his  performances  in  it?  Probably, 
it  was  merely  by  a slip  of  the  tongue  that  one  of  our  artists 
testified  in  a police  court  that,  in  his  opinion,  the  exhibi- 
tion not  of  the  finished  product  of  the  studio  but  of  the 
undressed — one  might  say— -skeleton  of  the  studio  would 
be  eminently  appropriate  for  a Broadway  shop-window. 
But  the  remark  was  an  unmistakable  manifestation  of  a 
tendency.  There  have  been  times  when  it  was  thought 
in  bad  taste,  even  with  reference  to  things  never  con- 
sidered so  in  themselves,  for  a man  to  talk  “ shop  ” or  to 
act  “ shop  ” or  in  any  way  to  thrust  his  “ shop  ” upon 
public  attention.  But  evidently  those  times  have  passed. 
Even  now,  however,  a logical  mind  ought  to  recognize 
the  difference  between  arguing  with  reference  to  what 
may  be  necessary  to  support  the  life  of  art,  and  arguing 
with  reference  to  how  much  the  remains  of  that  which 
has  been  denuded  of  what  might  properly  be  termed  its 
meat  can  contribute  to  sanitary  effects — to  sweetness  and 
enlightenment,  when  thrown  out  of  the  front  window 
onto  the  public  pavement. 

The  truth  is  that,  in  this,  as  in  every  other  practical 
possibility,  there  is  no  end  worth  seeking,  whether  it 
be  the  representation  of  human  sentiment  or  of  skill  in 


112 


PROPORTION  AND  HARMONY. 


workmanship,  that  cannot  be  attained  without  going  to 
extremes.  When  one  thinks  of  this  fact,  and  of  the  liabil- 
ity, if  it  be  disregarded,  of  having  art  lower  its  aims,  or,  if 
not  this,  having  it  antagonize,  through  creating  false  im- 
pressions of  its  aims,  thousands  of  those  in  special  need  of 
its  influence, — in  other  words,  when  one  thinks  how  much 
might  be  gained  to  the  world,  and  how  little  can  be  lost, 
by  applying  in  this  sphere  the  same  common  sense  that 
all  men  are  expected  to  apply  in  other  spheres,  it  cer- 
tainly seems  strange  that  those  who  wish  to  make  the 
most  of  art  should  pursue  a course,  in  either  criticism  or 
production,  fitted  really  to  make  the  least  of  it. 

Before  closing  this  chapter,  it  may  be  well  to  remind  the 
reader  that  the  fact  that  the  whole  human  form  and  every 
part  of  it  owes  the  beauty  which  we  recognize  in  it  largely 
to  its  representation  of  a certain  phase  of  significance,  fur- 
nishes the  best  possible  explanation  for  those  discrepancies 
in  taste,  which  are  nowhere  more  apparent  than  in  the 
judgments  which  different  persons,  equally  cultivated, 
form  with  reference  to  precisely  the  same  human  propor- 
tions. These  judgments  differ  because  men  differ  in  their 
views  of  adaptability  and  fitness,  and  in  the  recollections 
which  they  associate  with  persons  characterized  by  cer- 
tain features  ; but  more  than  all,  because  they  differ  in 
their  feelings  of  companionship  with  those  possessing 
traits  which  these  features  represent.  Owing  to  one  or  the 
other  of  these  reasons,  there  are,  for  all  of  us,  certain 
forms  so  adjusting  themselves  into  the  framework  of 
vision  and  mind  that  they  fit  into  what  men  term  their 
ideals  as  into  a vise,  and  hold  sympathy  spellbound. 
Certain  movements  in  these  forms  seem  regulated  to  such 
a rhythm  that,  in  unison  with  it,  all  our  currents  of  vein 
and  nerve  leap  from  the  heart  and  brain  and  thrill  along 


DISCREPANCIES  OF  TASTE.  II3 

their  courses.  They  do  so  very  likely  because  of  the 
operation  of  those  universal  laws  of  vibration,  the  connec- 
tion between  which  and  the  effects  of  beauty  was  sug- 
gested in  Chapter  XII.,  and  also  in  Appendix  I.  of 
“ Art  in  Theory.”  But  the  exact  reason  lies  deeper  in 
nature  than  any  plummet  dropped  by  human  means  can 
fathom.  We  cannot  know  the  cause  any  more  than  what, 
when  all  conductors  are  in  place,  speeds  the  impulse  of  an 
electric  current.  We  only  know  that  a reason  exists  at  all 
because  of  the  results  which  we  experience.  J ust  as  certain 
organs  of  the  ear  or  eye  respond  and  glow  with  a sense  of 
complete  freedom  and  delight  in  the  presence  of  certain 
harmonious  elements  or  combinations  of  sounds  or  sights, 
so  does  the  spirit  as  a whole.  There  may  be  some  so 
constituted  physically,  or  so  incapable  of  analyzing  what 
they  feel,  that  they  confound  this  apprehension  of  beauty, 
which  only  we  are  now  considering,  with  something  less 
pure  and  elevating.  But  those  who  have  never  made 
their  souls  the  servants  of  their  bodies,  and  whose  aesthetic 
as  well  as  ethical  natures  have,  therefore,  developed  nor- 
mally, are  aware  that  the  influence  which  flows  from 
beauty  and  beauty  alone  is  different  in  kind  from  any- 
thing debasing,  and  allied  to  that  which  is  wholly  spirit- 
ual. It  is  not  without  strength  in  extreme  youth,  nor  lost 
in  old  age,  and  in  its  power  to  give  delight  and  even  to 
arouse  romance,  it  is  stronger,  often,  when  exerted  by 
man  upon  man  and  woman  upon  woman,  than  when 
exerted  by  one  upon  another  of  another  sex.  These 
aesthetic  effects,  when  they  reveal  their  sources  through 
the  outward  forms  in  which  they  are  expressed  and  em- 
bodied, do  this  mainly  through  what  we  term  the  pro- 
portions. What  if  these  latter  in  themselves  be  merely 

a collection  of  like  or  related  measurements?  Is  this  not 
8 


I 14  PROPORTION  AND  HARMONY. 

exactly  what  we  should  expect  of  anything  the  effects  of 
which  can  be  ultimately  traced  to  vibrations?  Cannot 
the  same  be  affirmed  not  only  of  the  minute  waves  that 
underlie  results  in  melody  and  harmony  of  tone,  but  even 
of  the  larger  waves  of  rhythm  ? And,  if  without  rhythm 
there  can  be  no  effective  music  or  poetry,  how  should 
there  be  effective  painting  or  sculpture  without  pro- 
portion ? 


CHAPTER  VIII. 


PROPORTIONS  OF  THE  HUMAN  FIGURE  PRACTICALLY 
CONSIDERED. 

Standard  of  Measurement  in  Rhythm  and  Proportion  as  Fixed  by  Con- 
gruity — Repetition  and  Alternation — Repetition  or  Likeness  of  Meas- 
urements— Reason  for  Satisfaction  in  Effects  of  Proportion — Not  the 
Usual  Explanation — But  not  Inconsistent  with  the  Conceptions  of  the 
Greeks — Criticism  of  Statements  with  Reference  to  them — Difference 
between  an  Apparent  and  a Real  Measurement — Exact  Value  of  the 
Statements  of  Vitruvius — How  to  Find  the  True  Greek  Theory — Quo- 
tation from  Vitruvius — What  it  Implies — The  Ratios  to  be  Considered 
a Result  of  Likeness — Measurements  of  the  Head  and  Face — The 
Greek  Type  of  Face  not  the  Only  one  Manifesting  Effects  of  Propor- 
tion— Nor  are  the  Methods  of  Subdividing  it  the  Ones  usually  Adopted 
— Or  Necessary  to  the  Recognition  of  Beauty — -More  Minute  Like  Meas- 
urements in  the  Front  Face — In  the  Side  Face — In  the  Form  when 
Fronting  one — Effects  of  High  Civilization  on  the  Wedge-Shape  of  the 
Form — The  Lower  Limbs  from  the  Front — From  the  Side — Other 
Related  Measurements — Measurements  according  to  Curvilinear  Stand- 
ards— Similar  Circumferences  Describing  Many  Different  Outlines — 
Elliptical  Figure  as  Described  about  the  Form  as  a Whole — Signifi- 
cance as  Represented  in  the  Form  of  a Man  and  of  a Woman — Prin- 
ciples of  Proportion  not  Creative,  but  Guides  to  the  Selection  of  Models 
— Affording  Aid  in  Determining  the  Pose — Proportion  merely  an  Ap- 
plication to  Measurements  of  the  Art-Methods  on  Page  3. 


HE  rhythm  of  a musical  composition  is  usually  fixed 


by  that  of  a few  notes,  definitely  suggestive  of 
a certain  phase  of  feeling.  These  notes  comprise  the 
theme,  from  which  the  whole  is  developed  ; and  their 
measures  furnish,  as  one  might  say,  the  standard  for  the 
measures  of  the  whole.  So  the  proportions  of  a whole 


II 6 PROPORTION  AND  HARMONY. 

human  figure  are  usually  fixed  by  those  of  a few  features, 
furnishing  the  standard.  The  vital  temperament,  for 
instance,  gives  a standard  measurement,  as  in  the  neck, 
waist,  hips,  and  calves,  that  in  itself  has  greater  width 
than  the  standard  measurement  of  the  mental  tempera- 
ment. Starting  with  whatever  may  furnish  the  standard, 
the  other  measurements  in  well  formed  figures  will  be 
found  to  be  in  proportion  to  it.  This  will  cause  the 
figures  to  fulfil  perhaps  more  definitely  than  any  other 
the  art-method  of  congruity,  already  discussed  between 
pages  104  and  107  of  Chapter  VII.  This  art-method,  oc- 
casioned as  it  is  (see  the  note  on  page  61,  also  the  chart 
on  page  3)  by  the  requirements  of  the  mind,  will  usually 
reveal  important  particulars  in  which  the  same  figures 
also  fulfil  the  more  commonly  noticed  methods  of  unity , 
order,  comparison , and  principality.  According  to  the 
chart  on  page  3,  the  primary  method  connected  with  the 
requirements  of  matter,  i.  e.,  of  the  material  of  which 
the  product  is  constructed,  is  repetition , and  an  important 
development  of  this,  as  influenced  by  the  variety  common 
to  all  things  in  nature,  is  alternation.  Concerning  this 
latter  something  will  be  said  later.  At  present,  it  is 
enough  to  point  out  that  it  is  a method  of  relieving  repeti- 
tion of  monotony  ; and,  in  its  application,  it  can,  at  times, 
without  detriment  to  the  unity  of  the  general  propor- 
tional effect,  introduce  into  the  same  product  two  appar- 
ently different  schemes  of  measurement.  For  instance, 
in  the  front  of  the  Greek  temple,  Fig.  10,  page  36,  the 
width  of  the  columns  represents  one  measurement,  and 
the  width  of  the  spaces  between  them  represents  another. 
So  the  wide  spaces  between  certain  of  the  lines  drawn 
horizontally  across  the  faces  in  Figs.  64  to  68,  on  pages  126 
and  127,  represent  one  measurement,  and  the  narrower 


HUMAN  PROPORTIONS. 


ii  7 

spaces  another.  In  such  cases,  there  is  usually  a certain 
recognizable  ratio  between  the  different  widths,  as  I : 2,  or 
2 : 3,  or  3 : 4.  But  notice  that  this  ratio  need  not  be  ex- 
pressible in  such  small  numbers  as  to  be  readily  made 
out.  In  a temple,  for  instance,  no  matter  how  the  width 
of  one  column  was  related  to  the  width  of  the  space  be- 
side it,  the  relation  of  the  one  to  the  other  would  be  rec- 
ognized to  be  precisely  the  same  as  the  relation  of  the 
next  column  to  the  next  space  beyond. 

Now  let  us  go  back  to  repetitioyi.  The  main  reason 
why  the  mind  is  satisfied  when  seeing  outlines  related  to 
one  another  as  1 : 2,  or  2:5,  is  because,  in  such  cases,  it 
recognizes  that  the  first  is  another  expression  for  1 : 1 — j—  1 , 
and  the  second  another  expression  for  i-}-i  : 1 —}—  I — 1 — (— 
1—)— 1.  In  other  words,  the  mind  takes  satisfaction  not  in 
the  ratio  per  se,  but  in  that  which  the  ratio  enables  it  to 
recognize,  which  is,  that  in  fulfilment  of  the  fundamental 
art-method,  measurements  have  been  put  together  which 
are  alike  as  to  their  parts. 

This  is  not  the  explanation  usually  given  for  effects  of 
proportion.  But  it  is  the  explanation  most  consistent 
with  that  usually  given  for  effects  of  rhythm  ; it  is  the 
explanation  most  consistent  with  all  the  methods  of  art 
as  unfolded  in  “The  Genesis  of  Art-Form,”  and  repre- 
sented in  the  chart  on  page  3 of  this  volume  ; and,  finally, 
it  is  the  explanation  which  can  render  most  easy  and 
simple  the  practical  application  of  the  principle  to  all 
possible  visible  effects. 

It  can  readily  be  shown,  too,  that  this  explanation  is 
not  inconsistent  with  the  conceptions  which  the  Greeks 
must  have  had  of  the  subject.  In  commenting  upon  the 
testimony  of  the  Roman  writer  Vitruvius,  in  his  “ De  Ar- 
chitectural’ Samson,  in  his  “ Elements  of  Art-Criticism,” 


1 1 8 


PROPORTION  AND  HARMONY. 


book  in.,  chapter  i.,  summarizes  certain  of  these  concep- 
tions as  follows  : “ The  entire  statue  was  eight  heads  or 
ten  faces  ; and  one  half  the  statue  was  above  the  os 
pubis.  The  breadth  of  the  shoulders  was  two  heads;  of 
the  loins,  one  head  and  one  nose;  of  the  thighs,  one  head 
and  two  noses.  The  length  of  the  arm  was  three  heads, 
one  and  one  half  from  the  shoulder  to  the  elbow,  and  one 
and  one  half  from  the  elbow  to  the  first  knuckles.  From 
the  thigh  to  the  knee  was  two  heads,  and  the  same  from 
the  knee  to  the  ankle,  and  the  foot  was  one  head  and  one 
nose.  The  depth  of  the  chest  was  one  head  and  one  third 
of  the  nose ; of  the  loins,  three  and  one  third  noses.  The 
breadth  of  the  upper  arm  was  one  and  one  half  noses, 
front  view,  and  two  noses,  side  view;  of  the  lower  arm, 
in  the  thickest  part,  one  and  one  half  noses,  and  of  the 
wrist,  one  nose.  The  depth  of  the  thigh  was  three  noses; 
of  the  calf  of  the  leg,  two  noses  ; of  the  ankle,  one  nose.” 

Some  of  these  measurements,  as  will  be  noticed,  are 
carried  out  in  Figs.  31,  page  57,  and  32,  page  58.  Others, 
like  the  last  mentioned,  are  indefinite.  The  statement 
is  true  if  the  ankle  be  viewed  from  the  front,  but  false 
if  it  be  viewed  from  the  side ; and  just  the  opposite 
is  true  with  reference  to  the  wrist.  The  measurements 
have  been  quoted  here,  not  so  much  on  their  own  ac- 
count, as  on  account  of  the  testimony  which  they  furnish 
to  the  fact  that,  with  the  Greeks,  all  the  members  of  the 
form  were  viewed  in  their  relations  to  a unit, — as  stated  in 
this  case,  to  the  nose,  which  to  the  Greeks  represented  one 
third  of  the  face,  or  one  fourth  of  the  head. 

As  for  the  details  of  this  statement  of  Vitruvius,  we 
must  be  cautious  about  trusting  to  them  too  implicitly. 
Among  the  dimensions  mentioned,  take  “the  depth  of  a 
head  and  one  third  of  a nose.”  If  the  Greeks  really  made 


GREEK  MEASUREMENTS  FOR  THE  BODY.  I 19 

any  such  law,  it  may  have  been  because  the  peculiar  shape 
of  the  member  to  which  it  was  applied  made  it  necessary 
slightly  to  increase  the  real  dimension  in  order  to  manifest 
a sufficient  apparent  dimension,  one  head  and  one  third  of 
a nose  in  one  position  appearing  no  longer  than  a head 
alone  would  in  another.  It  is  beyond  question,  as  will 
be  shown  in  Chapter  XIV.,  that,  in  applying  the  princi- 
ples of  proportion  to  architecture,  the  Greeks  cared  less 
for  like  measurements  than  for  producing  the  appearance 
of  them  ; and  probably  the  same  would  be  true  when 
applying  these  principles  to  the  human  form. 

Moreover,  it  is  important  to  notice  that  an  apparent 
measurement  necessitates,  at  times,  not  only  a different 
result  from  an  actual  measurement,  but  also  a different 
conception  of  what  should  be  measured.  As  an  instance 
of  a different  result,  consider  how  the  leg  between  the  heel 
and  the  place  where  it  separates  from  the  body  is  appar- 
ently divided  at  the  knee  into  two  equal  parts.  This  is 
not  a result  of  having  the  half  below  the  knee  of  the  same 
length  as  the  half  above  it.  Being  slimmer,  the  lower  half 
would  appear  longer,  were  it  not  in  reality  slightly  shorter. 
Again,  as  an  instance  of  a different  conception,  consider 
the  measurement  of  the  ankle.  Ordinarily,  we  should 
suppose  this  to  be  a dimension  determined  by  its  circum- 
ference. But,  when  considering  effects  of  appearances,  it 
is  not  the  circumference  that  concerns  us,  but  the  appar- 
ent distance  from  one  side  of  the  ankle  to  its  other  side, 
as  it  is  seen  from  a single  point  of  view. 

With  this  thought  in  mind  let  us  turn  again  to  the 
opinions  of  the  Greeks,  quoting,  in  order  to  suggest  what 
these  opinions  were,  from  Vitruvius.  He  can  furnish  us 
with  testimony  sufficient  for  our  purpose,  even  though  we 
admit,  as  we  must,  that  his  authority  is  not  the  best.  He 


120 


PROPORTION  AND  HARMONY. 


was  an  architect,  not  a sculptor.  He  was  a Roman  too; 
and,  as  has  been  proved,  he  was  not  fully  informed  with 
reference  to  the  Greek  laws  even  of  architecture.  Be- 
sides this,  the  passages  in  which  he  refers  to  the  propor- 
tions of  the  human  form  are  introduced  into  his  work  as 
illustrations,  the  argument  being  that  as  the  human  fig- 
ure has  fixed  proportions,  so,  too,  a building  should  have 
them.  He  mentions  a few  of  these  proportions,  but  there 
is  no  evidence  that  he  even  intended  to  mention  them  in 
any  categorical  way.  These  facts  show  that  what  is  of 
value  in  his  testimony  is  less  what  he  says  than  what  he 
implies, — namely,  that  there  was  an  opinion  in  his  time, 
that  the  Greeks  had  a theory  that  the  proportions  of  hu- 
man figures  are  determined  by  comparative  measurements, 
and  that  they  based  their  practice  upon  this  theory. 

But  what  were  these  proportions,  and  what  principles 
did  they  fulfil?  Toward  answering  this,  the  statements 
to  be  quoted  may  give  us  hints.  The  principles  under- 
lying all  the  art-methods,  as  unfolded  in  “ The  Genesis  of 
Art-Form  ” and  summarized  on  page  3 of  this  volume, 
may  interpret  these  hints  ; and  a tape  measure  assiduously 
used  upon  the  existing  Greek  statues,  as  has  been  done 
by  the  author,  may  test  the  accuracy  of  the  interpretation. 
“ Nature  has  so  fashioned  a well  formed  human  figure,” 
says  Vitruvius,  in  book  iii.,  chapter  i.,  of  his  “ De  Archi- 
tectural’ as  translated  by  Joseph  Gwilt,  “that  in  the  face 
from  the  tip  of  the  chin  to  the  forehead  or  to  the  roots  of 
the  hair  is  a tenth  part  of  the  height  of  the  whole  body. 
From  the  chin  to  the  crown  of  the  head  is  an  eighth  part 
of  the  whole  height  [see  Figs.  31,  page  57,  32,  page 
58,  and  45,  page  86],  and  from  the  nape  of  the  neck  to 
the  crown  of  the  head  the  same.  From  the  upper  part 
of  the  breast  to  the  roots  of  the  hair,  a sixth;  to  the 


GREEK  MEASUREMENTS  FOR  THE  BODY. 


121 


crown  of  the  head,  a fourth.  A third  part  of  the  height  of 
the  face  is  equal  to  that  from  the  chin  to  the  under  side 
of  the  nostrils  ; and  thence  to  the  middle  of  the  eyebrows, 
the  same  ; from  the  last  to  the  roots  of  the  hair,  where  the 
forehead  ends,  the  remaining  third  part.  The  length  of 
the  foot  is  the  sixth  part  of  the  height  of  the  body  ; the 
forearm,  a fourth  part  ; the  width  of  the  breast  a fourth 


FIG.  62.— WHOLE  HUMAN  FORM  AS  RELATED  TO 
THE  CIRCLE. 

Seepages  15,  59,  121,  130,  132,  133,  141. 


part.  The  navel  is  naturally  placed  in  the  centre  of  the 
human  body,  and  if,  when  a man  is  lying  with  his  face 
upward  and  his  hands  and  feet  extended,  from  his  navel 
as  a centre  a circle  be  described,  it  will  touch  his  fingers 
and  toes.”  (See  Fig.  62  above.)  “ Measuring  from  the 
feet  to  the  crown  of  the  head  and  then  across  the  arms 


122 


PROPORTION  AND  HARMONY. 


fully  extended,  we  find  the  latter  measure  equal  the 
former ; so  the  lines  at  right  angles  to  each  other  enclos- 
ing the  figure  will  form  a square.”  (See  Fig.  63.) 


FIG.  63.— WHOLE  HUMAN  FORM  AS  RELATED 
TO  THE  SQUARE. 

See  pages  15,  59,  122,  130,  131,  141. 


In  this  quotation,  as  will  be  noticed,  we  again  have 
certain  parts  of  the  form  taken  as  standards  of  measure- 
ment, i.  e.,  the  face  and  head,  though  not,  as  on  page  118, 
the  nose.  Notice  also  the  note  at  the  bottom  of  this 
page.1  Neither  this  quotation  from  Vitruvius,  however, 

1 In  this  connection,  the  following  note  xviii.  of  Sir  Joshua  Reynolds 
on  Fresnoy’s  “Art  of  Painting”  may  be  of  interest.  From  the  note  a few 
clauses  in  which  the  proportions  mentioned  are  the  same  as  in  the  quotation 
from  Vitruvius  on  page  120  are  omitted. 

Verse  145. 

Learn  then  from  Greece,  ye  youths,  Proportion’s  law, 

Informed  by  her  each  just  position  draw. 

Du  Piles  has,  in  his  note  on  this  passage,  given  the  measures  of  a human 


MEASUREMENTS  OF  THE  BODY. 


123 


nor  this  note,  nor  any  usual  method  of  presenting  the 
subject,  seems  to  get  down  to  the  fundamental  source  of 
the  artistic  effect  involved,  which  is  the  satisfaction  de- 
rived by  the  mind  from  perceiving  certain  dimensions 
put  with  others  that  are  like  them,  or  are  exact  multiples 
of  them.  Nevertheless,  that  this  satisfaction  is  really  the 

body,  as  taken  by  Fresnoy  from  the  statues  of  the  ancients,  which  are  here 
transcribed  : 

“ The  ancients  have  commonly  allowed  eight  heads  to  their  figures, 
though  some  of  them  have  but  seven  ; but  we  ordinarily  divide  the  figure 
into  ten  faces.1 

From  the  chin  to  the  pit  betwixt  the  collar-bones  are  two  lengths  of  a 
nose. 

From  the  pit  betwixt  the  collar-bones  to  the  bottom  of  the  breast,  one 
face. 

From  the  bottom  of  the  breasts  to  the  navel,  one  face.2 

From  the  navel  to  the  genitories,  one  face.3 

From  the  genitories  to  the  upper  part  of  the  knee,  two  faces. 

The  knee  contains  half  a face. 

From  the  lower  part  of  the  knee  to  the  ankle,  two  faces. 

From  the  ankle  to  the  sole  of  the  foot,  half  a face. 

A man  when  his  arms  are  stretched  out  is  from  the  longest  finger  of  his 
right  hand  to  the  longest  of  his  left  as  broad  as  he  is  long. 

From  one  side  of  the  breast  to  the  other,  two  faces. 

The  bone  of  the  arm  called  the  Humerus  is  the  length  of  two  faces  from 
the  shoulder  to  the  elbow. 

From  the  end  of  the  elbow  to  the  root  of  the  little  finger,  the  bone  called 
Cubitus,  with  part  of  the  hand,  contains  two  faces. 

From  the  bone  of  the  shoulder-blade  to  the  pit  betwixt  the  collar-bones, 
one  face. 

If  you  would  be  satisfied  in  the  measure  of  breadth,  from  the  extremity 
of  one  finger  to  the  other,  so  that  this  breadth  should  be  equal  to  the  length 
of  the  body,  you  must  observe  that  the  boxes  of  the  elbow  with  the  humerus, 

1 This  depends  on  the  age  and  quality  of  the  persons.  The  Apollo  and  Venus  de’ 
Medici  have  more  than  ten  faces. — R. 

2 The  Apollo  has  a nose  more. — R. 

3 The  Apollo  has  half  a nose  more  ; and  the  upper  half  of  the  Venus  de’  Medici  is  to  the 
lower  part  of  the  belly,  and  not  to  the  privy  parts. — R. 


124 


PROPORTION  AND  HARMONY. 


source  of  the  artistic  effect  is  implied  in  all  the  quotations 
that  have  been  used,  and  will  be  confirmed  by  the  results 
of  a tape  measure  tried  upon  any  large  number  of  classic 
statues. 

It  has  been  pointed  out  that  we  could  not  recognize 
that  a nose  on  a given  face  was  out  of  proportion,  unless 
in  the  same  face,  near  the  nose,  were  something  with  which 
to  compare  it.  It  is  equally  true  that  we  could  not  recog- 
nize the  fact  readily,  unless  there  were  something  with 
which  we  could  compare  the  nose  exactly,  i.  e. , something 
which,  as  a rule,  is  of  exactly  the  same  length.  Notice 
again,  now,  that  we  could  not  recognize  the  fact  as  well  if 
there  were  only  one  other  feature  of  like  length  in  the 
face,  as  if  there  were  many  features.  The  same  principle 
applies  to  every  member  of  the  form.  And  the  readiness 
with  which  all  people  recognize  a lack  of  proportion  in 
any  member,  proves  the  presence  of  many  features  of  like 
dimensions  with  the  one  that  is  the  subject  of  adverse 

and  of  the  humerus  with  the  shoulder-blade,  bear  the  proportion  of  half  a 
face  when  the  arms  are  stretched  out. 

The  sole  of  the  foot  is  the  sixth  part  of  the  figure. 

The  hand  is  the  length  of  the  face. 

The  thumb  contains  a nose. 

The  inside  of  the  arm  from  the  place  where  the  muscle  disappears,  which 
makes  the  breast  (called  the  Pectoral  muscle),  to  the  middle  of  the  arm,  four 
noses. 

From  the  middle  of  the  arm  to  the  beginning  of  the  hand,  five  noses. 

The  longest  toe  is  a nose  long. 

The  two  utmost  parts  of  the  teats,  and  the  pit  betwixt  the  collar-bones  of 
a woman,  make  an  equilateral  triangle. 

For  the  breadth  of  the  limbs,  no  precise  measures  can  be  given,  because 
the  measures  themselves  are  changeable,  according  to  the  quality  of  the  per- 
sons and  according  to  the  movement  of  the  muscles.” — Du  Piles. 

The  measures  of  the  ancient  statues  by  Audran  appear  to  be  the  most 
useful,  as  they  are  accompanied  with  the  outline  of  the  figures  which  are 
most  distinguished  for  correctness. — R. 


LIKE  BODILY  MEASUREMENTS. 


125 


criticism.  Ordinarily,  no  one  can  tell  what  these  features 
are,  nor  which  of  their  dimensions  are  used  as  a basis 
of  comparison,  but  that  they  exist  is  beyond  question. 
Otherwise  men  could  not  make  the  comparisons  that  are 
so  common.  The  bearing  of  this  upon  the  subject  be- 
fore us,  of  course,  is  that  proportion  is  determined  by 
likeness,  of  which  the  ratios  are  a result,  not  a cause. 
Where  certain  features  are  as  1 : 1 and  1 : 2,  and  so  on, 
there  we  necessarily  have  conditions  that  lead  to  the 
other  simple  ratios. 

Applying  what  has  been  said  to  the  human  form,  as 
represented  both  by  the  Greeks  and  by  modern  artists, 
and  considering,  first,  rectilinear,  and,  later,  curvilinear 
measurements,  we  find  that,  in  spite  of  the  variations 
already  indicated  as  necessarily  existing,  there  is  a general 
tendency  to  like  measurements  or  exact  multiples  of  them 
in  the  following  cases. 

To  begin  with  the  head  and  face,  Fig.  45,  page  86,  shows 
five  like  horizontal  measurements  at  the  level  of  the  eyes, 
two  filled  by  the  eyes  themselves,  two  by  the  spaces,  as 
seen  from  the  front,  between  the  eyes  and  the  ears,  and 
one  filled  by  the  width  of  the  nose.  Three  other  like 
horizontal  measurements  may  be  seen  at  the  level  of  the 
mouth,  one  filled  by  the  main  outlines  of  the  mouth, — not 
including  all  of  them, — and  the  other  two  by  the  spaces 
on  each  side  between  the  mouth  and  the  sides  of  the 
cheeks.  Another  like  horizontal  measurement  may  be 
seen  also  at  the  nostrils,  and  still  another  at  the  lowest 
point  of  the  chin.  The  same  figure  shows  like  vertical 
measurements  between  the  top  of  the  head  and  the  top 
of  the  forehead,  also  between  this  and  the  bridge  of  the 
nose,  also  between  this  and  the  nostrils,  and,  again, 
between  these  and  the  chin. 


126 


PROPORTION  AND  HARMONY. 


These  measurements  conform  to  the  Greek  type  of 
face,  which  this  figure,  and  Fig.  69,  page  128,  are  supposed 
to  represent.  It  must  not  be  inferred,  however,  that  all 
faces,  in  order  to  meet  the  requirements  of  proportion, 
need  to  be  similar.  In  its  way,  a dog’s  face  may  exem- 
plify proportion  as  well  as  a man’s;  and  there  is  no  reason 
why  one  human  face  should  not  exemplify  it  as  well  as 
another,  though  differing  from  it  almost  radically.  This 
is  so  because  proportion  need  not  always  be  carried  out 


FIG.  65.— FACIAL  DIVISIONS. 
See  pages  116,  126,  127,  128. 


by  divisions  of  exactly  the  same  kind.  For  instance, 
none  of  the  spaces  in  Figs.  64  and  65,  or  in  Figs.  66, 
67,  and  68,  page  127,  are  vertically  divided  in  the  same 
way  as  in  Figs.  45,  page  86,  and  69,  page  128.  Nor,  as 
compared  with  one  another,  are  all  the  spaces  in  Figs. 
64  to  68  divided  in  the  same  way.  Yet  they  are  all 
divided  so  that  certain  measurements  in  each  are  like  one 
another.  The  like  measurements,  moreover,  which  are 
illustrated  in  Figs.  64,  66,  and  67,  are  such  as,  probably, 


LIKE  BODILY  MEASUREMENTS. 


127 


half  the  people  in  the  world,  without  ever  having  been 
aware  of  it,  have  been  in  the  habit  of  perceiving.  In  other 
words,  they  have  been  in  the  habit,  when  looking  at  a face, 
of  comparing,  mentally,  the  distance  between  the  chief 
line  of  the  eyebrows  and  of  the  eye,  with  the  distance 
between  the  nostrils  and  the  mouth,  and  also  of  compar- 
ing, above  and  below  these  narrower  spaces,  the  wider 
distances  between  the  hair  and  the  eyebrows,  the  eyes 
and  the  nostrils,  and  the  mouth  and  the  chin.  These  nar- 
rower distances  are  usually  to  the  wider  as  1:2,  though, 


FIG.  66.  FIG.  67. 

FACIAL  DIVISIONS.  FACIAL  DIVISIONS. 

See  pagse  116,  126,  127,  See  pages  116,  126, 
128.  127,  128. 


FIG.  68.— FACIAL  DIVISIONS. 

See  pages  116,  126,  127, 
128,  130. 


in  accordance  with  the  principle  of  alternation  as  explained 
on  page  1 1 6,  it  is  not  absolutely  necessary  that  the  ratio 
between  the  two  should  be  expressible  in  just  these  num- 
bers. All  that  is  necessary  is  that  the  third  measure- 
ments should  seem  alike,  and  that  the  intervening  ones 
should  seem  sufficiently  unlike  these  others  not  to  confuse 
the  mind  by  suggesting  likeness  where  it  is  not  supposed 
to  be  suggested. 

If  the  reader  will  examine  Figs.  64  to  68,  and  then  re- 


128 


PROPORTION  AND  HARMONY. 


call  his  own  experiences,  when  judging  of  faces,  he  will 
probably  be  ready  to  admit  that,  much  as  has  been 
made  of  the  Greek  vertical  divisions  of  the  face  as  in  Fig. 
45,  page  86,  and  Fig.  69,  few  persons  now  think  of  com- 
paring either  the 
height  of  the  fore- 
head, or  the  length 
of  the  nose,  with 
the  distance  be- 
tween the  nostrils 
and  the  chin.  More- 
over, if  they  do  com- 
pare these,  and  find 
all  of  equal  meas- 
urement, they  do 
not,  usually,  in  case 
they  are  Americans,  admire  the  arrangement,  and  for  a 
very  good  reason.  It  fails  to  represent  the  face  to  which 
they  are  the  most  accustomed,  or,  to  go  deeper,  it  fails  to 
represent  the  characteristics  by  which  they  are  most  at- 
tracted. The  longer  Greek  nose  (see  Chapter  VII.  of 
“ Painting,  Sculpture,  and  Architecture”)  represents  less 
emotive  susceptibility  than  a shorter  nose,  and  the  shorter 
Greek  chin  represents  less  will-power  than  a longer  chin. 
As  a rule,  the  American  does  not  admire  the  degree  of  mod- 
eration— the  calculating  tact — of  the  Greek  face ; but  he 
does  admire  plenty  of  will-force,  which  he  calls  character 
and  which  he  supposes  to  be  necessary  in  order  to  steady 
the  tendency  of  a more  susceptive  temperament. 

For  these  reasons,  when  he  tells  us  that  he  considers 
the  faces  in  Figs.  64  to  68  more  beautiful  than  those  con- 
forming to  the  Greek  type,  he  is  justified.  According  to 
the  laws  of  form,  properly  interpreted,  such  faces  fulfil 


LIKE  BODILY  MEASUREMENTS. 


129 


equally  with  the  Greek — though  according  to  a different 
method — the  principles  of  proportion.  But,  besides  this, 
according  to  the  laws  of  significance,  as  derived  from  his 
association  with  faces  of  the  ordinary  American  type,  from 
his  deductions  with  reference  to  the  characteristics  mani- 
fested by  them,  and  from  his  sympathy  with  the  persons 
possessing  such  characteristics,  it  is  in  complete  fulfilment 
of  aesthetic  principles  (see  Chapter  XIII.  of  “ Art  in 
Theory  ”)  to  say  that,  while  as  beautiful  in  form  as  are 
the  Greek  faces,  their  beauty,  to  one  of  the  race  and 
country  to  which  they  belong,  is  enhanced  on  account  of 
its  significance. 

In  many  faces,  as  in  Fig.  45,  page  86,  there  are  a 
number  of  measurements  more  minute,  which  a front 
view  of  the  face  will  show  to  be  alike  ; for  instance,  the 
vertical  distance  from  the  eyebrow  to  the  upper  lid  of  the 
eye,  and  then  from  this  across  the  eye  to  its  lower  lid, 
each  of  which  distances  again  seems  to  be  one  half  the 
horizontal  width  of  the  eye  (1  : 2).  The  distance,  too, 
from  the  nostrils  to  the  opening  of  the  mouth  seems  to 
be  the  same  as  between  this  and  the  dimple  under  the 
lower  lip;  and  the  ear  and  the  nose,  too,  are  often  upon 
the  same  level,  and  of  the  same  length. 

If  we  look  at  the  side  of  the  face,  as  in  Fig.  69,  page  128, 
we  find  that  the  eye  is  back  from  the  bridge  of  the  nose, 
the  nostril  back  from  the  point  of  the  nose,  and  the  side 
of  the  mouth  from  its  centre  just  about  the  same  distance, 
while  the  eyebrows  extend  back  about  twice  as  far  (r  : 2). 
Other  facts  which  are  true  of  what  we  Americans  consider 
symmetrical  features,  but  which  not  only  our  own  artists 
but  also  the  Greeks,  with  all  their  keenness  of  observation, 
seem  to  have  entirely  overlooked,  are  that  the  horizontal 
lines  formed  by  the  front  of  the  eyebrows,  by  the  lower 


130  PROPORTION  AND  HARMONY. 

lid  of  the  eye,  by  the  lower  line  of  the  nose,  and  by  the 
mouth  are  parallel  (Figs.  64,  page  126,  and  68,  page  127), 
and  that  the  downward  slope  of  the  ear  also  is  parallel  to 
that  of  the  nose,  with  which  it  also  corresponds  in  length. 
See  Figs.  64,  page  126;  68,  page  127;  and  69,  page  128. 
In  order  to  bring  out  this  effect,  this  latter  figure,  which 
was  supposed  to  represent  the  Greek  type,  had  to  be 
altered  when  transferred  to  this  book. 

Returning  to  a front  view  of  the  body,  we  find  that  the 
whole  length  of  the  head  is  apparently  the  same  as  that 
of  the  hand,  measuring  the  latter  not  from  the  bottom  of 
the  palm,  but  farther  up  the  arm,  above  the  wrist  joint,  at  the 
place  where  bracelets  are  usually  worn.  See  Figs.  31,  page 
57;  32,  page  58  ; 43,  page  82  ; 62,  page  121  ; 63,  page  122  ; 
and  71,  page  134.  This  is  the  place  which,  when  the  arms 
are  bare,  attracts  the  attention  of  the  eye,  and  seems  to 
be  the  dividing  point  between  hand  and  arm.  The  height 
of  the  face  below  the  hair  is  the  same  as  the  length  of  the 
hand  to  the  bottom  of  the  palm.  The  inside  of  the  arm 
from  armpit  to  wrist,  as  described  two  sentences  above, 
seems  to  be  twice  the  length  of  the  hand,  as  described  in 
the  same  sentence,  i.  e.,  2:  1 (Figs.  31,  page  57,  and  32,  page 
58.)  In  a man,  the  distance  from  shoulder  to  shoulder  is 
at  times  the  same  as  this  last  measurement  of  the  arm  ex- 
cluding the  hand,  i.  e.,  as  1 : 1 (Fig.  63,  page  122).  The 
inside  measurement  of  the  leg  from  trunk  to  heel  seems  to 
be  twice  this  same  measurement  of  the  arm  excluding  the 
hand,  i.  e.,  as  2 : 1 (Fig.  31,  page  57).  Or,  if  we  choose,  we 
can  look  at  the  outside  measurement  of  the  arm  from 
the  wrist  to  the  side  of  the  shoulder ; and  this  we 
shall  find  to  be  one  half  of  the  outside  measurement  of 
the  leg  from  the  ankle  to  the  highest  point  of  the  hip. 
Notice,  in  this  connection,  what  is  said  in  the  note  on 


LIKE  BODILY  MEASUREMENTS.  1 3 I 

page  123.  The  dimensions  given  there  do  not  disagree 
with  those  just  indicated,  but  are  calculated  differently. 
The  inside  measurements,  however,  seem  to  be  the  best 
suited  for  our  purpose.  It  is  they  that  determine  the 
visible  length  of  each  limb  when  at  rest.  It  is  because  of 
them  that,  when  the  arms  are  stretched  straight  outward 
and  the  man  stands  on  tiptoe,  there  are  just  eight  dimen- 
sions of  the  head  or  of  the  hand  measured  from  above  the 
wrist  both  in  the  height  of  the  figure  and  also  between 
the  tips  of  fingers  on  either  side  of  the  body  (Fig.  63,  page 
122).  The  centre  of  this  height  is  apparently,  but  seldom 
actually,  the  bottom  of  the  trunk  where  the  legs  separate 
from  it.  At  this  place,  the  width  of  the  body  is  of  course 
twice  that  of  the  legs  when  they  separate  (2  : 1).  The 
waist  is  about  half  the  distance  between  this  and  the  arm- 
pits,  and,  in  a man,  its  apparent  width  is  about  twice  that 
of  each  of  the  legs,  when  measured  at  the  same  distance  be- 
low the  bottom  of  the  lower  extremity  of  the  trunk  as 
the  waist  is  above  this  (Figs.  31,  page  57;  32,  page  58; 
and  63,  page  122.)  Sometimes,  as  if  the  arms  were  merely 
cut  out  with  curves  from  the  sides  of  the  body,  the  waist 
itself  appears  to  be  narrower  than  the  shoulders  by  the 
widest  combined  width  of  the  two  elbows,  each  of  which 
sustains  to  it  a simple  ratio,  and  in  large  numbers  of  men 
of  our  own  time,  the  hips  seem  to  be  narrower  than  the 
shoulders  merely  by  the  width  of  the  two  wrists,  each  of 
which  also  sustains  a simple  ratio  to  them.  See  Fig.  31, 
page  57. 

It  is  interesting,  by  the  way,  to  notice  the  effect  which 
high  degrees  of  civilization  seem  to  have  upon  the  forms 
of  men.  If  we  walk  on  an  American  street,  we  can 
scarcely  find  one  whose  form  corresponds  to  that  in 
Fig.  43,  page  82,  nor  many  whose  forms  correspond  to 


132 


PROPORTION  AND  HARMONY. 


that  in  Fig.  44,  page  84.  One  reason  for  this,  probably, 
is  that,  in  civilized  countries,  growing  boys  exercise  their 
arms  less  and  sit  down,  as  in  studying,  more.  It  is  worth 
noticing,  too,  that,  accompanying  this  physical  change, 
there  has  come  a suggestion — in  certain  cases,  not,  of 
course,  in  all  of  them,  nor  in  any  of  them  except  in  a 
very  general  way — of  a psychological  change.  The  man 
acquires  a larger  number  of  womanly  traits,  becoming 
what  is  termed  a gentleman.  How  far  a corresponding 
change  takes  place  in  a woman,  as  she  becomes  more  in- 
tellectually independent,  is  a question.  But  it  is  a fact 
that,  in  the  opinion  of  most  American  artists,  a woman’s 
hips  should  be  of  the  same  breadth  as  her  shoulders, 
whereas,  in  the  opinion  of  most  English  artists,  the  hip- 
measurement  should  be  the  greater. 

There  is  as  much  diversity  in  the  measurements  of  the 
lower  limbs  as  of  the  trunk.  Viewed  from  in  front,  the 
calf  below  the  knee  is  often  of  the  same  width  as  is  that 
part  of  the  leg  which  is  just  as  far  above  the  narrowing  of 
the  lower  limb  below  the  knee  as  the  calf  is  below  this 
point.  See  Figs.  43,  page  82  ; 44,  page  84;  54,  page  100; 
and  57,  page  103.  The  width  of  the  calf,  as  seen  in  front, 
is  usually  twice  that  of  the  ankle  (2  : r),  which  latter  is  the 
same  as  the  width  of  the  instep  below  the  ankle-bone,  i.  e., 
1 : 1 (see  Figs.  49,  page  95,  and  57,  page  103);  and  the 
centre  of  the  foot  is  usually  of  the  same  width  as  is  that 
part  of  the  leg  which  is  at  the  same  distance  as  it  is  from 
the  narrowest  part  of  the  ankle  ( 1 : 1 ) and  of  the  same 
width  also  as  is  the  palm  of  the  hand  (1  : 1).  See  Fig.  62, 
page  121.  Viewed  from  the  side  (see  Fig.  70,  page  133), 
the  calf  of  the  leg  is  usually  of  the  same  width  as  is  that 
part  of  the  leg  which  is  at  the  same  distance  above  thenar- 
rowing of  it  j ust  below  the  knee  as  the  calf  is  below  this  nar- 


LIKE  BODILY  MEASUREMENTS. 


133 


row  point ; and  sometimes  the  width  of  the  calf  is  the  same 
as  is  the  diagonal  distance  from  the  top  of  the  instep  to  the 
heel(t  : 1).  This  last  measurement  is 
very  variable  ; but  one  reason  why  a 
high  instep  is  generally  admired, 
seems  to  be  because  it  enables  the  eye 
to  perceive  a resemblance  between  this 
dimension  at  the  ankle  and  the  dimen- 
sion at  the  calf.  In  the  side  view  again, 
the  width  of  the  ankle  is  usually  as 
1 : 1 to  that  of  the  distance  from  the 
highest  point  of  the  instep  to  the  floor. 

It  is  about  as  2 : 3 — though  in  this 
Fig.  70  it  is  represented  as  1 : 2 — to 
the  width  of  the  calf ; and  it  is  as  1 : 2 
to  the  upper  length  of  the  foot  from 
the  top  of  the  instep  to  the  end  of 
the  toes.  See  Fig.  36,  page  71  ; Fig. 

70;  and  Fig.  75,  page  142.  The  upper 
length  of  the  foot  appears  to  be  the 
same  as  that  of  the  hand  from  the 
bottom  of  the  palm.  The  ankle  is  lo- 
cated a little  above  the  instep,  and  one 
wearing  bracelets  and  anklets  appears 
to  have  extremities,  i.  e.,  hands  and 
feet,  of  equal  lengths  (1  : 1). 

See  Figs.  71,  page  134;  also 
43-  Page  82  ; and  62,  page  121. 

The  sole  of  the  foot,  exclud- 
ing the  toes,  is  very  nearly 
the  length  of  the  hand,  as  ex- 
plained on  page  130;  and  though  we  are  told  that  according 
to  the  Greeks  the  length  of  the  whole  foot  of  a man  was  one 

o 


FIG.  70.— LEG  AND  FOOT. 
See  pages  132,  133. 

From  Duval’s  “ Artistic  Anatomy.” 


134 


PROPORTION  AND  HARMONY. 


sixth  of  the  height  of  the  body,  we  seldom  find  a foot  that 
is  relatively  as  long  as  this.  From  the  same  side  view  of 
the  body,  we  may  often  notice,  too,  a like  or  clearly  related 
width  in  the  neck  and  certain  parts  of  the  legs ; also  in 
the  head,  waist,  and  a certain  part  of  the  thigh  ; also  in 
the  breast  and  lower  trunk,  though 
generally,  especially  in  the  male,  these 
dimensions,  as  related,  respectively, 
each  to  each,  seem  gradually  lessened 
as  the  measurements  are  applied  to  a 
lower  part  of  the  form.  See  Figs.  35, 
page  70  ; 36,  page  71  ; and  37,  page  72. 

But  we  have  not  completed  our 
study  of  human  proportions,  when  we 
have  measured  them  according  to 
merely  rectilinear  standards.  The 
outlines  of  the  body  are  almost  invari- 
ably curved.  This  necessitates  meas- 
clothinq  proportional  urements  according  to  a curvilinear 

in  parts.  standard.  In  most  of  the  faces  of  the 

See  pages  82,  130,  133. 

Greek  statues,  the  curves  made  by  the 
outlines  of  the  top  of  the  skull,  the  hair  at  the  forehead, 
the  eyebrows,  eyes,  nostrils,  mouth,  and  chin,  can  be  reg- 
ularly described  on  either  side  of  parallel  horizontal  lines 
drawn  through  them.  See  Fig.  45,  page  86.  The  whole 
contour  of  the  face,  which,  as  viewed  in  front  in  Fig.  45, 
is  oval,  is  sometimes  represented  as  formed  upon  parts  of 
the  circumferences  of  three  circles  described  from  centres, 
one,  as  in  this  figure,  at  the  middle  of  the  forehead,  one 
at  the  bridge  of  the  nose,  and  one  at  the  nostrils.  If  we 
suppose,  as  is  usually  done,  that  the  three  circles,  one 
below  the  other,  are  diminished  according  to  regular  de- 
grees or  ratios  of  gradation  (see  chart  on  page  3,  also 


CURVED  MEASUREMENTS  FOR  THE  BODY.  1 35 

note  at  the  bottom  of  page  61),  then,  as  is  evident,  they 
fulfil  certain  aesthetic  requirements  very  literally.  In  a 
similar  way,  the  contour  of  the  head,  as  viewed  from  the 
side,  is  sometimes  represented  as  formed  upon  parts  of 
two  circumferences,  the  centre  of  the  larger  of  which  is  in 
the  middle  of  the  temple,  and  of  the  smaller  in  a straight 
line  back  of  this  and  immediately  above  the  ear.  The 
form  of  the  head,  however,  is  so  largely  determined  by 
the  mental  idiosyncrasies  of  individuals,  that  rules  of 
this  kind  can  have  only  a very  limited  fulfilment.  Fig.  69, 
page  1 28,  shows  a different  method  of  measurement.  The 
face  is  related  to  an  oval,  and  certain  parts  of  it  to  radi- 
ating lines  drawn  from  a point  back  of  the  ear.  No  such 
methods,  however,  are  of  invariable  applicability.  Per- 
haps their  chief  interest  lies  in  the  fact  that  they  all 
suggest,  in  a general  way,  the  existence  of  arrangements 
indicating  proportion  as  a possibility. 

What  seems  to  be  a more  regular  fulfilment  of  curvi- 
linear requirements,  the  author  has  observed  in  the  effects 
of  the  like  circumferences  drawn  about,  not  the  faces, 
but  the  forms  in  Figs.  31,  page  57  ; 32,  page  58  ; 35,  page 
70  ; 36,  page  71  ; 73,  page  137  ; and  74,  page  139.  These 
circumferences  describe,  of  course,  only  very  general  out- 
lines, in  accordance  with  the  principles  unfolded  in  pages 
68  to  72.  But,  even  as  applied  to  general  outlines,  the 
effects  indicated  are  far  too  numerous,  and  too  uniformly 
present,  not  to  be  seriously  considered  among  the  factors 
entering  into  the  proportional  result.  Were  the  likeness 
in  curvature  thus  suggested  absent  from  any  form,  the 
eye  would  recognize  the  fact,  and  miss  an  impression 
of  unity  to  such  an  extent  as  to  get  an  impression  of  de- 
formity. See  page  71.  We  may  accept  these  curves, 
therefore,  especially  when  taken  in  connection  with  the 


136  PROPORTION  AND  HARMONY. 

facts  of  binocular  vision  to  be  explained  in  Chapter  XVI. 
as  a testimony  to  the  aesthetic  impression  conveyed  by 
putting  like  measurements  with  like.  At  the  same  time, 
it  is  true  that,  in  all  cases,  when  examined  carefully,  the 
outlines  of  the  body,  after  conforming  to  these  circumfer- 
ences for  a distance  sufficient  to  establish  a certain  simi- 
larity of  curvature,  pass  into  other  forms  of  curvature, 
either  abruptly  or  gradual^,  and  very  often  in  exact  ful- 
filment of  the  principle  explained  on  pages  60  and  61  ; 


FIG.  72.— WOMAN’S  FORM  ENCLOSED  BETWEEN  CIRCLES. 

See  pages  59,  138,  290,  291,  295. 


in  such  a way,  therefore,  that  it  can  be  said  that  there  is 
an  exact  ratio  between  one  part  of  the  curve  and  each 
other  part  of  it.  Sometimes,  too,  as  between  the  calf 
and  the  knee,  the  thigh  and  the  waist,  the  forearm 
and  the  elbow,  and  the  upper  arm  and  the  shoulder, 
there  is  a distinct  likeness  in  the  method  characterizing 
all  the  changes  in  curvature.  In  fact,  the  whole  outer 
contour  of  the  leg  from  ankle  to  knee  seems  to  be  re- 
peated with  an  increment  between  the  knee  and  the  hip, 


FORMS  OF  MEN  AND  WOMEN. 


137 


as  well  as  also  between  the  ankle  and  the  hip,  and  the 
wrist  and  the  shoulder.  See  Figs.  31,  page  57;  32,  page 
58 ; and  73. 


FIG.  73.— MAN’S  FORM  ENCLOSED  BETWEEN  CIRCLES. 

See  pages  15,  59,  72,  S7,  135,  137,  138,  290,  291,  295. 


Now,  taking  a more  comprehensive  view,  we  shall  find 
that  the  form  of  both  a man  and  a woman,  as  seen  either 
from  the  front  or  the  side,  fits  into  a shape  which  may  be 
termed  elliptical  because  resembling  that  of  an  ellipse, 


138 


PROPORTION  AND  HARMONY. 


See  Figs  72,  page  136,  and  73,  page  137.  As  will  be  un- 
folded on  page  280  of  Chapter  XVI.  of  this  volume,  treat- 
ing of  harmony  of  outline,  there  is  an  aesthetic  reason  for 
this  elliptical  shape  aside  from  any  requirements  of  pro- 
portion. Confining  ourselves  at  present  to  only  these 
latter,  it  will  be  noticed  that  a man’s  form,  when  he  is 
facing  us,  requires  a more  broadened  elliptical  framework 
than  a woman’s.  His  form  from  the  shoulders  downward 
is  wedge-shaped,  the  shoulders,  as  a rule,  being  about 
as  much  wider  than  the  hips  as  these  are  than  the 
width  of  the  combined  calves,  and  as  these  latter  are  than 
the  width  of  the  combined  ankles.  That  is  to  say,  the 
ratio  of  decrease  in  all  these  cases  is  about  the  same,  thus 
manifesting  proportion  according  to  the  method  of  grada- 
tion, already  mentioned  in  the  note  on  page  61,  and  in 
the  chart  on  page  3.  A representation  of  this  wedge- 
shaped  formation,  as  we  usually  see  it,  will  be  found  in 
Fig.  31,  page  57.  A somewhat  exaggerated  illustration 
of  the  same  is  given  in  connection  with  Mr.  Hay’s  con- 
ception of  a typical  man  in  Fig.  73,  page  137.  Notice  in 
it  the  straight  lines  drawn  diagonally  downward  between 
the  outsides  of  the  shoulders  and  the  feet,  as  well  as  the 
other  straight  lines  at  either  side  of  the  body  moving  out- 
ward as  they  extend  toward  the  feet,  which  latter  lines 
connect  the  centres  of  the  different  inscribing  circles. 

A woman’s  form  is  perhaps  more  nearly  describable  in  an 
exact  ellipse  (see  Fig.  72,  page  136),  the  shoulders  being 
about  the  same  width  as  the  hips,  and  narrower  than  they 
are  when  combined  with  the  width  of  the  arms,  and  the 
relative  difference  between  the  width  of  the  hips  and  of 
the  combined  calves  being  greater  than  in  the  case  of  a 
man.  Compare  Figs.  31,  page  57,  and  73,  page  137,  with 
Fig.  74,  page  139. 


FORMS  OF  MEN  AND  WOMEN. 


139 


As  for  other  differences  in  human  shapes,  there  is  a rea- 
son for  this  one  too,  which  is  ascribable  to  significance. 
A larger  size  emphasizes  the  part  of  the  form  in  which  it 
appears.  That  which  is  of  chief  importance  in  a man  is 
strength,  and  strength  as  required  in  labor.  The  seat  of 
this  kind  of  strength  is  in  the  shoulders  that  control  the 
arms.  Therefore,  when  the  shoulders  are  broad  the  man 


FIG.  74.— WOMAN’S  FORM  ENCLOSED  IN  LIKE  CIRCLES. 
See  pages  15,  59,  72,  87,  135,  13S,  290,  295. 


appears  to  be  made  right.  Moreover,  the  shoulders, 
being  at  the  broadest  part  of  the  form,  naturally  attract 
our  attention  first.  But,  as  will  be  shown  on  pages  277  to 
280,  the  point  on  which  the  eyes  are  fixed  is  always  hori- 
zontal to  the  widest  part  of  the  outside  limits  of  distinct 
and  easy  vision.  In  order  to  conform  to  all  the  require- 


140 


PROPORTION  AND  HARMONY. 


ments  of  such  vision,  the  part  of  the  form  below  this  point 
must  taper  downward.  If  we  be  looking  chiefly  at  the 
shoulders,  this  wedge-like  shape  beneath  them  is  that 
which  best  meets  the  requirements  of  ease  of  vision.  On 
the  contrary,  that  which  is  of  chief  importance  in  a woman 
is  her  sympathetic  nature,  and  the  seat  of  this  is  in  the  torso 
sufficiently  below  the  shoulders  to  cause  the  same  require- 
ments of  ease  of  vision  to  be  best  fulfilled  when  the  wedge- 
like tapering  begins  lower  down  than  in  the  case  of  the 
man,  accompanied,  too,  by  a tapering  tendency  in  the 
direction  of  the  head. 

In  all  that  has  been  said,  reference  has  been  made  to 
only  very  general  outlines.  As  applied  to  any  but  these, 
and,  indeed,  to  some  extent,  even  to  them,  it  is  impossi- 
ble to  find  rules  for  guidance  which,  as  used  in  particu- 
lar cases,  do  not  constantly  need  to  be  authenticated  and 
modified  by  the  facts  that  can  be  learned  from  studying 
models.  All  art  is  the  representation  of  nature.  The  art 
that  portrays  human  nature  represents  that  which  is,  pre- 
sumably, the  highest  embodiment  of  creative  intelligence. 
A man  who  tries,  after  no  matter  how  faithful  a study  of 
the  human  form  in  general,  to  create  such  a form  de  novo , 
is  in  danger  of  representing  his  own  conceptions  to  the 
detriment  both  of  nature  and  of  that  creative  intelli- 
gence which  gives  human  nature  its  highest  significance. 
As  indicated  on  page  89,  a knowledge  of  proportion  can 
do  little  more  than  enable  an  artist,  in  the  presence  of 
models,  to  select  for  portrayal  features  that  are  beautiful, 
and,  where  these  are  combined  with  such  as  are  not,  to 
avoid  copying  the  latter,  or,  if  he  must  regard  them, 
then,  as  a result  of  observation  and  experience,  to  correct 
their  defects.  To  do  this  last  satisfactorily,  however,  or 
even  to  choose  a model  wisely,  requires  that  an  artist’s 


PROPORTION  IN  THE  POSE.  141 

judgment  should  be  regulated  by  some  correct  general 
theory. 

Such  a theory  may  afford  equal  aid,  too,  when  one  is 
called  upon  to  form  practical  or  theoretical  judgments 
with  reference  to  mere  posture.  Notice  how  exactly  most 
of  the  main  lines  in  Fig.  35,  page  70,  correspond  to  the 
circumferences  described  about  them.  A little  study  of 
the  forms  in  Figs.  43  to  47,  pages  82  to  92,  or  in  Figs.  49 
to  59,  pages  95  to  105,  will  reveal  similar  effects.  Observe, 
too,  the  long  simple  curve  between  the  right  armpit  and 
the  right  foot,  also  the  similar  but  compound  curve  be- 
tween the  left  hand  and  the  left  foot,  in  Fig.  75,  page  142. 
There  is  no  doubt  that,  when  limbs  are  arranged  so  that 
their  combined  outlines  suggest  these  like  curves,  the 
effect  of  beauty  is  enhanced  on  account  largely  of  their 
influence  in  producing  effects  not  only  of  harmony  of  out- 
line, but  of  proportion.  Indeed,  it  is  while  speaking  of 
methods  of  securing  these  effects,  that  Vitruvius  tells  us 
that:  “ Applying  the  principles  of  Geometry,”  the  Greeks 
“supposed  the  human  figure  with  the  arms  and  limbs  ex- 
tended to  be  first  enclosed  in  a square  or  a circle,  and 
then  in  a cube  or  sphere.  Standing  erect,  with  the  arms 
extended  at  right  angles,  the  height  of  the  body  from 
head  to  foot,  and  its  breadth  from  finger  end  to  finger 
end  being  the  same,  they  inscribed  it  within  a square 
[Fig.  63,  page  122];  while  with  the  arms  extended  ob- 
liquely but  symmetrically,  they  drew  the  human  figure 
with  the  hands  and  feet  in  the  circumference  of  a circle 
whose  centre  was  the  navel  [Fig.  62,  page  1 2 1 ] . Every 
posture  of  action,  as  in  walking,  running,  wrestling,  box- 
ing, was  then  mathematically  studied,  and  the  line  of  the 
centre  of  gravity  was  carefully  marked  ; when  the  posi- 
tion of  each  limb  and  the  breadth  of  each  portion  of  the 


142 


PROPORTION  AND  HARMONY. 


whole  frame  first  conceived  to  be  located  in  a circum- 
scribed circle  or  square,  and  then  in  an  enclosed  cube  or 
sphere,  was  measured  with  the  greatest  accuracy.”  Evi- 
dently, so  far  as  the  mind  is  influenced  by  the  appearance 
of  likeness  in  measurements,  or  in  the  outlines  manifest- 


FIG.  75.— FIGURE  FROM  NAUSICA.  E.  J.  POYNTER. 

See  pages  59,  133,  141,  369. 

ing  them,  it  is  essential  to  arrange  forms  in  pictures  and 
statues  so  that  their  general  features  shall  reveal  the 
effects  of  such  measurements. 

In  fact,  as  applied  to  any  of  the  products  of  the  fine 


PROPORTION  IN  THE  POSE. 


143 


arts,  it  seems  inevitable  that  our  general  conclusion  should 
conform  to  that  already  indicated,  which  is  that  propor- 
tion, while  necessarily  involving  the  use  of  such  ratios  as 
1:2,  2:3,  3 : 4,  4 : 5,  etc.,  is  nevertheless,  fundamentally 
considered,  no  more  than  an  application  to  measurements, 
and,  as  connected  with  these,  to  spaces,  of  the  methods 
of  art  already  described  in  “ The  Genesis  of  Art-Form,” 
and  developed  in  the  order  in  which  they  are  arranged  in 
the  chart  on  page  3 of  this  volume. 


CHAPTER  IX. 


PROPORTION  IN  ARCHITECTURE. 


The  Study  of  Proportion  is  still  more  Essential  to  the  Architect  than  to  the 
Painter  or  Sculptor — Ways  in  which  a Building  may  be  Given  Ex- 
pression and  Character — The  Essential  Condition  of  Form  is  the 
Grouping  of  Factors  that  in  Part  are  Alike — Architectural  Likeness  by 
Way  of  Congruity — of  Repetition,  Alternation,  Consonance,  Inter- 
change, Gradation,  etc. — All  these  Methods  maybe  Applied  to  Measure- 
ments— Ratios  of  Measurements  Recognizable  when  Expressed  in  Small 
Numbers — This  Fact  as  Applied  to  an  Exterior — To  Interiors — Rela- 
tive Measurements  Need  to  be  Apparent — Apparent  Measurements 
Differ  with  Circumstances — Effects  Produced  by  Apparent  Subdivisions 
—Horizontal  Subdivisions  as  Indicated  by  Outlines — Vertical  Sub- 
divisions— Horizontal  as  Related  to  Vertical  Subdivisions — Influence  of 
Subdivisions  as  Counteracting  Real  Dimensions  by  Apparent  Ones. 


RCHITECTURE,  like  music,  deals  with  forms  that 


to  only  a limited  extent  can  be  said  to  result  from 
an  imitation  of  nature.  In  some  regards,  this  fact  gives 
the  builder  greater  freedom  for  invention  than  is  possible 
in  painting  and  sculpture.  He  is  not  expected  to  accept 
forms  as  he  finds  them.  Like  the  musician,  who  is  at 
liberty  to  shorten  and  lengthen  sounds  so  as  to  make  them 
rhythmical,  he  is  at  liberty  to  shorten  and  lengthen  shapes 
so  as  to  make  them  proportional.  But  this  fact  places 
him,  in  some  regards,  under  peculiar  restraints.  If  the 
effects  of  the  proportions  produced  by  him  must  depend 
upon  his  own  invention,  it  is  particularly  necessary  for 
him  to  understand  what  the  right  proportions  should  be. 


144 


PROPORTION  IN  ARCHITECTURE. 


145 


A painter  not  knowing  this  may  succeed  because  he  may 
be  able  to  copy  accurately  the  proportions  of  objects  that 
form  his  models.  But  the  architect,  barring  the  instances, 
necessarily  limited,  in  which  he  may  exactly  imitate  the 
buildings  of  others,  must  design  his  own  forms.  In  such 
circumstances,  so  far  as  beauty  depends  on  proportion,  if 
ignorant  of  its  requirements,  he  will  fail  as  certainly  as  a 
musician  attempting  to  compose  a march,  without  know- 
ing how  to  produce  rhythm.  To  show  this  fact,  as  well 
as  the  effects  that  proportion,  in  such  cases,  can  add  to  a 
structure,  and  the  places  where  it  can  be  introduced,  let 
us  consider,  for  a moment,  in  accordance  with  the  line  of 
thought  unfolded  in  full  in  Chapters  XVII.  to  XIX.  of 
“ Painting,  Sculpture,  and  Architecture  as  Representative 
Arts,”  some  of  the  possible  ways  in  which  a building  may 
be  treated. 

To  begin  with,  it  may  be  made  to  appear  to  be  no  more 
than  a uniformly  constructed  blank  wall.  In  this  form, 
of  course,  it  will  be  utterly  expressionless.  Altering  it 
for  the  better,  the  blankness  of  the  wall  may  be  inter- 
rupted by  lines  where  the  bricks  or  stones  composing  it 
are  joined.  These  will  give  it  some  expression,  but  not 
much.  Then  mouldings  may  be  run  along  the  base  and 
top  of  the  wall.  These  will  reveal  that  there  is  a founda- 
tion below  and  an  attempt  at  completion  above.  If  suf- 
ficiently massive,  they  may  impart  to  the  structure  as 
much  expression  as  we  find  in  the  old-fashioned  walls 
erected  around  ancient  cities.  See  Fig.  9,  page  36.  But 
besides  this,  openings  may  be  made  in  the  wall  for  doors 
and  windows,  and  a roof  placed  above  the  upper  mould- 
ing. These  will  show  it  to  be  designed  for  the  entrance 
of  objects,  and  of  light,  and  for  shelter.  Still  again,  to  the 
tops  and  bottoms  of  the  openings  maybe  added  elaborate 


146 


PROPORTION  AND  HARMONY. 


caps  and  sills.  These  will  emphasize  the  openings.  In 
addition  to  these,  between  the  windows  or  doors,  mould- 
ings may  be  carried  horizontally  around  the  building  or 
in  pilasters  or  buttresses  perpendicularly  up  and  down  its 
sides.  These  will  suggest  arrangements  designed  for  sup- 
port,— possibly  of  floors  dividing  the  building  into  differ- 
ent storeys,  or  of  partitions  dividing  it  into  different  rooms  ; 
and  thus  will  tend  to  reveal  the  kind  of  building  that  it  is. 
Finally,  the  outlines  of  the  roof  may  be  carried  up  into 
gables,  turrets,  domes,  spires;  and  thus  give  additional 
representation,  and  so  expression  and  character  to  the 
general  effect.  See  Fig.  76,  page  147  ; also  what  is  said  of 
certain  representative  features  of  this  building  on  pages 
349  and  352  of  “ Painting,  Sculpture,  and  Architecture  as 
Representative  Arts.” 

Notice,  however,  that,  even  yet,  all  may  not  be  done 
which  is  essential  in  order  to  make  the  form  of  the  build- 
ing, as  a form,  thoroughly  satisfactory.  As  brought  out 
in  “The  Genesis  of  Art-Form  ” and  in  this  volume  in  the 
note  at  the  bottom  of  page  61,  the  fundamental  require- 
ment of  form  as  form  is  the  putting  together  of  factors 
which,  notwithstanding  some  inevitable  differences,  are 
nevertheless  partly  alike.  In  its  endeavor  to  group  these 
features  into  organic  form , the  mind  combines  them  in 
accordance  with  such  methods  as  those  termed  in  the 
chart  on  page  3,  unity , variety , complexity,  order , con- 
fusion, counteraction , comparison , contrast,  complement, 
principality,  subordination,  and  balance. 

As  influenced  by  the  particular  requirements  of  each 
product,  the  artistic  tendency  is  first  exercised  through 
comparison  by  way  of  congruity  (page  3).  This  causes  parts 
that  are  to  be  alike  to  be  selected  so  that  they  shall  con- 
form to  the  mental  purpose  of  the  building.  In  the  degree 


WiiA 


FIG.  76.  — UNIVERSITY  AT  SYDNEY,  AUSTRALIA. 


148 


PROPORTION  AND  HARMONY. 


in  which  they  are  to  represent  that  which  is  heavy,  strong, 
immovable,  substantial,  dignified,  or  near,  congruity  gives 
them  all  a tendency  to  be  more  or  less  large  and  bulky; 
in  the  degree  in  which  they  are  to  represent  the  opposite, 
it  gives  them  an  opposite  tendency.  In  the  degree  in 
which  they  are  to  represent  repose,  congruity  makes  them 
characterized  by  horizontality  ; in  the  degree  in  which 
they  are  to  represent  aspiration,  it  makes  them  character- 
ized by  perpendicularity.  In  the  degree  in  which  they 
are  to  represent  thoughtful  contrivance,  congruity  makes 
them  straight  and  rectangular ; in  the  degree  in  which 
they  are  to  represent  more  emotive  effects,  it  makes  them 
irregularly  angular  or  curved.  Notice  these  facts  and 
others,  as  brought  out  in  Chapters  III.  to  VI.  of  “ Painting, 
Sculpture,  and  Architecture  as  Representative  Arts.” 

The  general  character  of  the  outlines  that  are  to  be 
associated  having  been  determined  by  the  mental  purpose, 
they  are  then  put  together  according  to  such  methods  as 
are  stated  in  the  chart  on  page  3,  and  in  the  note  at  the 
bottom  of  page  61,  prominent  among  which  are  repetition , 
alternation , consonance,  interchange,  gradation,  and  transi- 
tion. As  in  the  case  of  painting,  so  too  we  shall  find 
here  that  all  these  methods  may  be  applied  to  relative 
measurements  as  well  as  to  relative  shapes  ; and,  there- 
fore, to  the  production  of  effects  of  proportion.  These 
relative  measurements  are  usually  estimated  according  to 
heights,  lengths,  or  breadths  considered  in  perspective, 
but  sometimes  also  they  are  estimated  according  to  the 
directions  of  curves  or  acuteness  of  angles.  But  it  is  well  to 
notice  that  in  these  latter  cases,  it  is  wellnigh  impossible 
to  distinguish  such  effects  as  are  attributable  to  the 
measurements,  from  such  as  are  attributable  to  the  out- 
lines that  are  measured.  For  instance,  when  one  says 


PROPORTION  IN  ARCHITECTURE. 


149 


that  the  angles  described  by  the  coverings  over  the  gable- 
windows,  turrets,  and  different  parts  of  the  roof  in  Fig. 
27,  page  51,  are  not  in  proportion,  he  necessarily  refers 
to  appearances  produced  both  by  measurements  and  by 
shapes.  In  the  mind  of  the  observer,  therefore,  the  two 
different  classes  of  effects  are  often  confounded. 

In  order  to  develop  rightly  the  subject  that  is  to  be  con- 
sidered, let  us  try  to  start  with  a correct  conception  of  what 
architectural  proportion  requires;  and,  for  this  purpose, 
let  us  recall  what  was  said  of  it  in  Chapter  IV.,  page  39. 
It  was  there  stated  that  the  measurements  of  certain  parts 
of  a building  should  appear  to  be  related  to  one  another 
according  to  certain  ratios.  But,  in  order  to  appear  thus 
related,  it  was  pointed  out  that  the  ratios  should  be_such 
as  to  be  easily  recognized  ; and  that,  in  order  to  fulfil  this 
condition,  they  should  be  expressible  in  small  numbers. 
For  instance,  if,  in  a window,  or  in  a blank  space  inclosed 
by  mouldings,  or  in  the  interior  of  a room,  or  in  a whole 
facade,  the  height  be  to  the  breadth  as  I : 1,  I : 2,  2 : 3,  3 =4, 
etc.,  it  is  easy  to  recognize  that  the  two  are  in  proportion  ; 
but  if  they  be  to  one  another  as  5 : 1 1,  or  9 : 14,  or  12:17, 
etc.,  it  is  not  easy  to  recognize  this. 

An  illustration  of  what  is  meant,  as  well  as  of  one  or 
two  other  facts  necessary  to  point  out  here,  may  be  ob- 
tained by  glancing  at  Fig.  77,  page  150.  This  figure  is 
all  the  more  convenient  for  our  purposes,  because  of  its 
excess  of  ornamentation,  justifiable  to  some  extent,  how- 
ever, as  said  on  page  348  of  “ Painting,  Sculpture,  and 
Architecture  as  Representative  Arts,”  on  the  ground  of 
its  being  one  of  the  chief  entrances  to  the  palace  of  the 
Louvre.  Notice  that  if  we  represent  the  width  of  each 
large  window  by  2,  this  will  apparently  be  to  the  width 
of  the  space  between  the  window  and  the  nearest  pillar 


150 


PROPORTION  AND  HARMONY. 


as  2 : i ; to  the  width  of  the  space  occupied  by  the  two 
pillars  as  2:2;  to  the  height  of  the  window  as  2 14  ; to 
the  height  of  the  whole  storey  in  which  each  high  win- 
dow is  situated  as  2 : 5 ; to  the  height  of  the  triangular 
pediment  at  the  top  as  2 : 3 ; and  to  the  distance  that  the 

curved  part  of  the  roof  extends 
above  the  pediment  as  2 : 5.  These 
relationships  seem  apparent  to  a 
first  glance  and  to  recognize  them 
gives  us  a certain  degree  of  satis- 
faction. 

The  same  principle  is  true  as 
applied  also  to  interiors.  The 
proportions  of  some  rooms  are 
such  that  the  moment  that  we 
enter  them  they  give  us  satisfac- 
tion. Others  do  not.  What  the 
relationships  of  length,  breadth, 
and  height  should  be,  in  order  to 
produce  the  former  result,  has 
sometimes  been  stated  with  great  exactness.  Vitru- 
vius, for  instance  (see  page  1 19),  tells  us  that  the  length 
should  be  to  the  breadth  as  5 : 3,  or  as  3 : 2 ; in  very  large 
halls,  as  2:  1,  and  sometimes  as  5 : 7.  As  to  their  height, 
Peter  Legh,  in  the  “ Music  of  the  Eye  ” (see  page  27),  in 
commenting  on  Vitruvius,  says  : “ If  simple  analogies  are 
to  be  our  guide  in  all  the  eurithms  and  all  the  symmetries, 
the  best  rule  for  height  seems  to  make  it  equal  to  half 
the  sum  of  the  length  and  the  breadth ; these  would  be 
lofty  rooms,  but  lofty  rooms  are  always  handsome,  and 
this  system  would  always  give  us  a good  proportion,  for 
when  the  proportion  of  length  to  breadth  were  as  one  to 
two,  the  height  would  be  one  and  a half,  that  is  to  say, 


FIG.  77.— PAVILION  OF  RICHE- 
LIEU, PARIS. 

See  pages  42,  44,  149,  152,  154, 
158,  160,  162,  163,  175. 


PROPORTION  IN  ARCHITECTURE.  I 5 I 

the  breadth,  height,  and  length  would  be  respectively  two, 
three,  and  four.” 

Whatever  may  be  thought  of  these  and  other  like  state- 
ments, notice  that,  whether  applied  to  exteriors  or  interi- 
ors, the  important  consideration  is  that  there  should  be 
some  apparent  relationship  between  the  length,  height, 
and  breadth.  If  we  perceive  that  there  is  such  a relation- 
ship, our  minds  are  satisfied.  If  we  fail  to  perceive  it, 
they  are  confused  ; the  effects  are  distracting  and  dis- 
quieting. As  will  presently  be  shown,  the  use,  on  exteri- 
ors, of  window-caps,  string-courses,  cornices,  pilasters, 
pillars,  and  also  of  some  of  these,  as  well  as  of  color  and  of 
upholstery  in  interiors,  may  sometimes  counteract  a con- 
fusing tendency.  But  sometimes,  too,  it  cannot ; and 
when  needing  to  suggest  relationships  that  do  not  really 
exist,  it  can  never  do  so  except  by  apparently  shortening 
or  lengthening  actual  dimensions. 

This  last  sentence  will  remind  the  reader  of  what  was 
said  in  Chapter  IV.,  and  will  be  unfolded  further  in  Chap- 
ter XIV.,  namely,  that,  as  the  principles  of  proportion 
have  reference  to  appearances  and  to  these  alone,  they 
cannot  be  fulfilled  in  a satisfactory  way  without  regard  to 
circumstances.  A number  of  straight  lines  enclosed  within 
a space,  for  instance,  increase  the  apparent  length  of  that 
space  in  the  direction  in  which  they  point  or  incline.  Any 
other  spaces  containing  no  such  lines,  yet  intended  to  ap- 
pear of  equal  length  with  it,  ought  really,  therefore,  to  be 
a little  longer.  Again,  if  when  we  are  looking  at  a build- 
ing a projecting  cornice  hide  part  of  a wall,  window, 
pediment,  or  roof  that  is  above  the  cornice,  so  that 
this  upper  part  appears  too  short  or  too  low  to  be  in 
good  proportion,  then,  as  we  shall  find  was  the  case  in  the 
Parthenon,  it  must  be  made  longer  or  higher,  no  matter 


152 


PROPORTION  AND  HARMONY. 


FIG.  78  —ARCH  OF  SEPTIMIUS  SEVERUS. 

See  pages  152,  163,  175. 


what  its  real  measurement  may  be.  The  end  to  be  at- 
tained is  not  factors  with  like  or  related  measurements, 
but  factors  that  appear  to  have  these. 

To  illustrate  this  statement,  by  referring  again  to  Fig. 
77,  page  150,  as  we  look  at  this  facade  it  appears  to  be— 

though  it  is  not — construct- 
ed according  to  a ratio  of 
breadth  to  height,  if  we  in- 
clude the  rounded  part 
above  the  pediment,  of  2 : 4; 
or,  if  we  do  not  include  this, 
of  2:3.  But  the  height  is 
not  relatively  so  great  as 
these  figures  would  indicate. 
It  merely  appears  to  be  so  ; 
and  one  reason  for  this  is 
the  cumulative  effects  of  the 
perpendicular  lines  of  the  pillars.  Similar  effects  will  be 
noticed  in  Fig.  78,  above.  To  many,  this  arch  seems 
to  be  exactly  as  high  as  it  is  broad,  but  it  is  not.  This  is 
true,  however,  of  the  arch  in  Fig.  79,  page  153,  and  of  the 
temple  in  Fig.  80,  page  153  ; but  the  pillars  in  both  these 
latter  make  the  height  seem  greater  than  the  breadth. 

There  is  another  fact  worth  noticing  in  connection  with 
the  facade  in  Fig.  77,  page  1 50.  This  fact  is,  that  we  judge 
the  whole  breadth  to  be  related  to  the  whole  height  as 
1 : 2,  or  as  2 : 4,  because  of  the  effect  produced  upon  the 
mind  by  the  smaller  spaces  into  which  the  whole  is  sub- 
divided. The  clear  inference  from  this  is  that  the  mind 
judges  of  the  proportions  of  a whole  from  the  propor- 
tions of  the  parts  composing  it ; precisely,  indeed,  as  it 
judges  of  rhythm  as  a whole  from  the  separate  effects  of 
the  measures  as  it  hears  them,  one  after  the  other.  It  is 


A R CHI  TECT  UK  A L PROP  OR  TI  ON  S. 


153 


needless  to  say  that  this  is  not  the  method  usually  attrib- 
uted to  judgments  formed  of  proportion.  Critics  gener- 
ally start,  rather  than  end,  by  saying  that  the  height  of 
the  Parthenon  is  to  its  breadth  as  9 : 14.  But  it  is  a ques- 
tion whether  the  mind,  however  rapidly  it  works,  does  not 
draw  its  conclusions  from  a comprehensive  glance,  first, 
at  details.  Look,  for  instance,  at  the  facade  of  the  Cathe- 
dral of  Cologne,  Fig.  81,  page  155.  Considering  each 
long  window  with  the  moulding  under  it  to  represent 
one  storey,  we  may  say  that  the  height  of  the  two  towers, 


Seepages  152,  163.  Seepages  152,  154,  163,  164,  168, 

175. 


exclusive  of  the  finial  at  the  extreme  top  of  the  spires, 
is  equal  to  that  of  six  storeys.  As  a fact,  each  storey  is 
slightly  less  in  height  than  the  storey  under  it,  an  arrange- 
ment which,  while  not  introducing  sufficient  difference  to 
lessen  the  appearance  of  likeness  in  the  dimensions,  does 
increase  the  apparent  altitude  of  the  building,  because,  if 
a dimension,  apparently  meant  to  be  the  same,  seems  to 
be  slightly  less,  it  appears  to  be  at  a greater  distance.  So 


154 


PROPORTION  AND  HARMONY. 


we  may  say  that  the  height  of  this  cathedral  represents 
that  of  six  storeys.  The  height  of  the  nave — as  seen  be- 
tween the  towers — -exclusive  of  a finial  resembling  that 
at  the  top  of  the  spires,  may  be  said  to  represent  the 
height  of  two  storeys  and  one  half ; though,  as  a fact — 
with  no  addition,  it  may  be  said,  to  the  artistic  effect  of  the 
building — it  is  slightly  more  than  this.  The  reason  why 
the  nave  has  an  upper  one-half  storey  seems  to  be  because 
its  gable,  to  correspond  in  pitch — one  cannot  help  saying 
that  it  might  correspond  still  more  closely  in  pitch — to  the 
other  angular  outlines  of  the  building,  needs  to  be  just  half 
as  high  as  a whole  storey.  Therefore,  though  we  may  say 
that  the  height  of  the  nave  is  to  the  height  of  the  towers 
as  5 : 12,  it  is  not  of  this  proportion,  as  a cause,  that  the 
mind  thinks  when  looking  at  the  building,  but  of  the  smaller 
as  well  as  general  arrangements  of  the  building  which  make 
this  proportion  a result. 

Now  notice,  once  more,  that  arrangements  such  as  have 
been  indicated,  especially  in  Fig.  77,  page  150,  illustrate 
what  was  said  on  page  43,  of  the  effect  produced  upon  the 
mind  when  determining  ratios,  by  outlines  dividing,  ac- 
cording to  some  unit  of  measurement,  the  parts  to  be 
compared.  Relative  measurements  may,  of  course,  be  in- 
dicated merely  by  the  width  of  windows  and  doors.  But 
it  is  evident  that  these  measurements  can  be  more  clearly 
indicated,  when  emphasized  by  other  vertical  or  horizontal 
indications  of  subdivision.  In  Willesden  Church,  Fig.  14, 
page  40,  the  width  of  the  tower  and  of  the  church  is  the 
same,  giving  two  equal  divisions.  In  St.  Stephen’s,  Caen, 
Fig.  1 1,  page  37,  the  width  of  each  tower  and  of  the  space 
between  the  two  towers  is  the  same,  giving  three  equal 
divisions  in  width,  as  there  are  also  in  the  temple  in  Fig. 
80,  page  153.  In  St.  Sulpice,  Paris,  Fig.  82,  page  156,  con- 


FIG.  81.— COLOGNE  CATHEDRAL — FACADE.  155 

See  pages  42,  44,  153,  154,  156,.  157,  160,  163,  165,  175,  180,  207, 
226,  236,  237. 


156 


PROPORTION  AND  HARMONY. 


cerning  which,  however,  something  more  will  be  said 
presently,  each  tower  is  exactly  half  as  wide  as  the  space 
between  the  towers,  giving  four  equal  divisions;  and  in  the 
temple  of  Theseus,  Fig.  io,  page  36,  as  also  in  the  cathe- 


FIQ.  82.— ST.  SULPICE,  PARIS. 

See  pages  42,  43,  44,  154,  158,  160,  161,  166,  175. 


dral  at  Cologne,  Fig.  81,  page  155,  we  can  see  five  equal 
divisions.  Notice,  in  the  latter  building,  how  artistically 
effects  of  variety  and  balance  are  introduced  without  in- 
terfering at  all  with  this  appearance  of  exact  subdivision. 


ARCHITECTURAL  PROPORTIONS.  I *7 

In  the  side  divisions,  one  of  the  huge  buttresses  flanking 
the  towers  is  joined  with  each  of  the  comparatively  narrow 
windows  of  the  towers  ; but,  in  the  central  division,  there 
are  no  large  buttresses  and  the  central  window  fills  almost 
the  entire  width. 


FIQ.  83.— ST.  SULPICE  MODIFIED. 
See  page  161. 


What  is  true  of  horizontal  divisions  is  true,  of  course, 
of  vertical  ones.  The  six  storeys  in  Cologne  Cathedral 
have  already  been  noticed.  Similar  divisions  need  hardly 


158 


PROPORTION  AND  HARMONY. 


be  pointed  out  in  St.  Sulpice,  Fig.  82,  page  156.  In  Chi- 
chester Cathedral,  Fig.  15,  page  41,  the  two  bands  divid- 
ing the  spire  into  three  equal  parts  of  the  same  height  as 
the  square  part  of  the  tower  above  the  roof,  indicate,  at 
once,  the  proportion  of  3:1.  In  Fig.  76,  page  147,  there 
are  many  different  ways  in  which  the  horizontal  string- 
courses, by  dividing  the  spaces,  feveal  the  fact  of  appar- 
ently like  or  related  measurements.  It  is  these  that,  by 
separating  into  two  subdivisions  the  distance  between  the 
windows  of  the  first  and  of  the  second  storeys,  cause 
this  space  to  seem  the  same  as  the  space  also  divided  into 
two  subdivisions,  between  the  top  of  the  second-storey 
windows  and  the  top  of  the  castellation  above  the  eaves. 
It  is  these  string-courses  too  that  cause  the  large  gable  over 
the  bay  windows  at  the  left  to  appear  to  add  a third 
storey  to  the  building  of  exactly  the  same  height  as  each 
of  the  two  storeys  below  it,  and  that  cause  the  four 
storeys  of  the  central  tower,  and  the  five  storeys  of  its  cor- 
ner turrets,  all  to  seem  of  the  same  height.  On  pages  349 
and  352  of  “ Painting,  Sculpture,  and  Architecture  as  Rep- 
resentative Arts,”  these  string-courses,  and  other  features 
of  this  exterior,  are  shown  to  be  artistic  because  they  rep- 
resent the  arrangements  of  storeys  and  rooms  in  the 
interior.  Now  they  are  shown  to  be  so  for  a reason  that 
has  nothing  to  do  with  such  representation.  This  is  only 
one  more  of  many  illustrations  of  the  fact  that  genuinely 
artistic  effects  usually  accord  equally  with  the  requirements 
both  of  form  and  of  significance. 

Now  let  us  observe  in  what  complex  ways  (see  page  15) 
these  outlines,  emphasizing  the  subdivisions,  work  together 
to  indicate  the  ratios  between  horizontal  and  vertical 
measurements  in  facades  as  wholes.  In  Fig.  77,  page  1 50, 
the  square  formed  by  all  of  the  building  that  is  under  the 


PROPORTION  IN  ARCHITECTURE. 


*59 


string-course  immediately  above  the  windows  in  the  second 
storey  seems  to  be  divided  in  height  into  two  parts  and  in 
width  into  three  parts.  In  each  part,  the  width  seems  to 
be  to  the  height  as  2 : 3.  The  2 of  the  three  widths  multi- 


FIG.  84.— ST.  SULPICE  MODIFIED. 

See  page  161. 

plied  by  3 give  6 parts  for  the  whole  square ; and  the  3 
of  the  two  heights  multiplied  by  2 also  give  6 for  the 
whole.  This  equality  of  results  suggests  another  reason 
why  this  space  below  the  third  storey  seems,  as  said  on 


i6o 


PROPORTION  AND  HARMONY. 


page  152,  to  be— although  it  is  not — just  as  wide  as  it  is 
high,  i.  e.,  square.  In  Cologne  Cathedral,  Fig.  81,  page 
155,  it  was  shown,  on  page  154,  that  the  height  of  the  nave 
appeared  to  be  to  the  height  of  the  towers  as  5:12.  On 
page  156  the  width  was  shown  to  be  apparently  divided 
into  5 parts.  Therefore  the  width,  too,  of  the  building 
appears  to  be  to  the  height  of  the  towers  as  5 : 12  ; while 
to  the  height  of  the  nave,  it  appears  to  be  as  5 : 5,  or  as 
1 : 1. 

The  inference  drawn  from  the  subdivisions  is  more 
accurate  as  applied  to  the  Cathedral  of  Cologne  than  to 
the  pavilion  in  Fig.  77,  page  150,  but  in  neither  case  can 
the  mind  escape  from  a mistaken  impression.  It  cannot 
believe  that  the  proportions  are  one  thing,  when  the  sub- 
divisions suggest  that  they  are  another.  A very  convinc- 
ing proof  of  this  may  be  obtained  from  the  facade  of  St. 
Sulpice,  Paris,  Fig.  82,  page  1 56.  Has  any  one  ever  looked 
at  this  church  without  finding  himself  involuntarily  asking 
why  it  is  that  its  proportions  seem  so  unsatisfactory? 
And  yet  it  is  not  because  the  measurements,  as  applied 
to  the  building  as  a whole,  violate  any  of  the  principles  of 
proportion.  The  extreme  width  of  each  tower  is  to  the 
width  of  the  space  between  the  towers  exactly  as  1:2. 
Could  any  scheme  of  ratios  be  more  simple?  Why,  then, 
does  it  not  appear  so  ? Why,  but  because  of  the  five 
divisions  made  by  the  pillars  in  the  space  between  the 
towers?  How  can  the  mind  recognize  that  each  tower’s 
width  is  to  the  space  as  I : 2,  or,  what  is  the  same 
thing,  as  2 : 4,  when  it  sees  five  instead  of  four  divisions  in 
this  space  ? It  cannot  do  so,  or,  at  least,  not  without  at 
first  being  confused.  Were  there  a pediment  above  the 
cornice  over  the  nave,  the  apex  of  this  would  divide  the 
space  there  into  two  equal  parts ; or  were  the  central  door 


PROPORTION  IN  ARCHITECTURE. 


161 


of  the  nave  made  more  prominent  than  the  two  doors 
each  side  of  it,  then  the  present  unfortunate  effect  would 
be  prevented.  But  if  such  changes  cannot  be  made,  the 
mind  would  be  better  satisfied,  in  that  it  would  judge  the 
proportions  to  be  more  correct,  even  on  a supposition  that 
they  were  2 : 4,  in  case  there  were  only  four  arches  between 
the  towers,  as  in  Fig.  83,  page  157  ; though,  in  fact,  the 
proportions  would  be  less  correct.  Or,  if,  instead  of  four 
arches,  which  are  objectionable  because  allowing  no  cen- 
tral door,  there  were  three  arches,  as  in  Fig.  84,  page  1 5q, 
with  these  again  the  mind  would  be  satisfied,  but  for  a 
different  reason.  A single  glance  at  this  Fig.  84  reveals 
the  fact  that  neither  of  the  towers  is  as  wide  as  the  cen- 
tral space  between  them,  and  yet  is  not  twice  as  wide. 
The  three  arches,  as  well  as  the  open  space  higher  up 
between  the  towers,  give  an  impression  that  each  tower  is 
to  this  space  as  2 : 3,  besides  which,  as  the  towers  are 
much  nearer  together  than  in  Fig.  82,  page  156,  the  mind 
is  more  easily  reconciled,  according  to  the  principle  of 
balance , to  an  arrangement  of  the  arches  in  the  towers 
different  from  that  shown  in  the  space  between  them. 


CHAPTER  X. 


PROPORTION  IN  ARCHITECTURE,  CONTINUED. 

The  Mind  Takes  Satisfaction,  not  in  Ratios,  but  in  the  Repetition  of  Meas- 
urement Indicated  by  them — This  Form  of  Repetition  Illustrated — 
Repetitions  of  Measurements  and  Shapes  Go  together — Illustration  of  an 
Absence  of  both  Forms  of  Repetition — Alternation  of  Measurements — 
Consonance  as  Applied  to  Shapes — Interchange  as  Applied  to  Shapes — 
A Unique  Illustration  of  it — Consonance  and  Interchange  as  Applied  to 
Measurement — An  Illustration  of  them  and  of  Complication — Grada- 
tion of  Shapes  and  Measurements — Complement  and  Balance  of  Shapes 
and  Measurements — Proportion  an  Application  to  Measurements  of  the 
Art-Methods  Mentioned  on  Page  3. 


HE  conclusion  reached  in  the  last  chapter  will  serve 


to  verify  a statement  made  many  times  already,  to 
the  effect  that  the  main  reason  why  the  mind  takes  satis- 
faction in  seeing  outlines  related  to  one  another  as  I : 2 or 
2 : 3,  etc.,  is  because  it  recognizes  that  the  first  is  another 
expression  for  1 : 1 -{-  1,  and  that  the  second  is  another  ex- 
pression for  1 — J—  1 : 1 — (—  1 — (—  1 . In  other  words,  the  mind 
does  not  take  satisfaction  in  the  ratio  per  se,  but  in  per- 
ceiving the  fulfilment  of  the  art-method  of  repetition  as 
applied  to  measurements.  It  is  not  too  much  to  say  that 
the  main  impression  with  reference  to  proportion  con- 
veyed by  Fig.  77,  page  150,  is  that  of  likeness  in  certain 
spaces  occupied  by  the  various  openings  as  surrounded 
by  pillars  or  mouldings. 

Now  observe  the  same  fact  as  exemplified  in  the  primitive 
manifestations  of  proportion  illustrated  in  Figs.  6,  page  33  ; 
7,  page  34  ; 8,  page  35  ; and  9,  page  36.  Observe  the  fact 


REPETITION  IN  ARCHITECTURAL  PROPORTION.  163 

as  exemplified  also  in  the  artistic  manifestations  of  the  same 
characteristics  in  Figs.  10,  page  36;  ii.page  37;  12,  page 
38;  15,  page  41  ; 30,  page  55;  76,  page  147;  77,  page  150; 
and  81,  page  155.  Similar  repetition  is  evident,  too,  in  con- 


FIQ.  85.— AN  AMERICAN  CHURCH. 

See  pages  164,  166. 

nection  with  just  enough  of  that  variety  which  the  Greek 
knew  so  well  how  to  introduce,  in  Fig.  80,  page  153,  as 
well  as  in  the  Roman  arches  in  Figs.  78,  page  152,  and 
79,  page  153. 

Most  of  these  figures  will  recall  and  exemplify  what 
was  said  on  page  148,  with  reference  to  the  artistic  neces- 


164 


PROPORTION  AND  HARMONY. 


sity  of  repetition  in  shape  as  well  as  in  measurement. 
Here  it  is  chiefly  important  to  notice  how  inevitably  the 
two  kinds  of  repetition  go  together.  Fig.  27,  page  51, 
was  used  in  order  to  illustrate  how  an  absence  of  one 
kind  of  it  involves  an  absence  of  the  other.  Notice  the 
same  fact  now  as  illustrated  in  Fig.  85,  page  163. 

Not  only  do  the  horizontal  caps  of  the  upper  windows 
in  the  apse  fail  to  correspond  to  the  arched  caps  in  the 
same,  but  the  distance  between  these  upper  caps  and 
the  roof  fails  to  correspond  to  any  other  vertical  distance 
in  the  apse.  So,  too,  not  only  does  the  lower  large 
arch  of  the  large  tower  fail  to  correspond  in  shape  to  the 
other  arches  of  the  tower,  bu.t  the  distance  from  it  to 
the  twin  arches  under  it,  as  well  as  to  the  horizontal  sill 
of  the  large  arched  window  over  it,  fails  to  correspond 
to  any  other  vertical  distance  in  the  tower.  The  same  is 
true,  also,  of  the  relative  heights  of  different  spaces  in 
the  small  tower.  How  a man  could  construct  a building 
supposing  that  the  eye  would  not  immediately  recognize 
and  resent  these  incongruities  in  the  shapes  and  measure- 
ments is  inexplicable.  But  one  is  forced  to-sav  that  this 
is  often  done,  and — what  is  worse — is  done  by  those  con- 
sidered to  be  our  foremost  architects. 

The  repetition  .of  measurements  as  influenced  by  the 
art-methods  of  variety  or  alteration  (see  chart  on  page  3) 
is  wellnigh  certain,  as  intimated  on  page  116,  to  pass  into 
more  or  less  alternation  of  measurements.  For  instance, 
the  pillars  in  Figs.  10,  page  36,  and  80,  page  153,  alter- 
nate with  the  spaces  between  the  pillars.  In  such  cases, 
if  all  the  pillars,  as  compared  with  one  another  and 
not  with  the  spaces  between  them,  are  of  like  apparent 
dimensions,  and  also  all  the  spaces,  as  compared  with  one 
another  and  not  with  the  pillars,  then  it  is  not  necessary 


ARCHITECTURAL  PROPORTIONAL  ALTERATION.  1 65 

that  the  ratio  between  the  dimensions  of  the  pillars  and 
the  dimension  of  the  spaces  should  be  easily  recognized; 
in  other  words,  it  is  not  necessary  that  this  ratio  should  be 
represented  by  a small  number  (see  page  1 17).  Whatever 
may  be  the  ratio,  the  mind  will  take  in  at  a glance  the 
fact  that  one  pillar  is  to  the  space  next  to  it  as  a second 
pillar  is  to  a second  space. 

Accordingly,  while  it  may  be  desirable  that  the  meas- 
urements of  each  set,  whether  of  pillars  or  spaces,  should 
sustain  a certain  relationship  to  the  measurements  of  each 
other  set,  this  is  much  less  important  than  that  the  meas- 
urements of  all  the  members  of  each  set  should  seem  to 
be  alike.  To  illustrate  what  is  meant,  it  is  important  in 
Fig.  15,  page  41,  that  the  two  dark  bands  surrounding 
the  spire  should  both  seem  of  the  same  height  as  the 
ornamentation  at  the  top  of  the  square  part  of  the  tower, 
also  that  the  larger  spaces  of  the  spire  should  seem  of  the 
same  height  as  the  square  part  of  the  tower  between  the 
roof  and  this  ornamentation.  But  it  is  less  important 
that  the  exact  ratio  between  these  bands  and  the  larger 
spaces  should  be  recognized.  So  in  Fig.  76,  page  147,  it 
is  important  that  the  two  subdivisions  between  the  front 
windows  of  the  first  and  second  storeys  should  seem  the 
same  as  the  two  subdivisions  between  the  tops  of  the 
windows  of  the  second  storey  and  the  top  of  the  whole 
front  wall.  But  it  is  less  important  that  the  exact  ratio 
between  the  height  of  these  spaces  and  the  height  of  the 
windows,  or,  say,  of  the  breadth  of  the  windows,  should 
be  recognized.  So  again,  in  Cologne  Cathedral,  Fig.  81, 
page  155,  it  is  important  that  the  storeys,  as  they  have 
been  termed,  should  seem — though  gradually  diminished 
in  order  to  increase  the  apparent  height — of  like  height, 
and  that  the  same  should  seem  to  be  the  case  with  the 


PROPORTION  AND  HARMONY. 


1 66 

cornices  or  mouldings  separating  these  storeys  ; but  it  is 
less  important  that  the  exact  ratio  between  the  height  of 
the  storeys  and  the  height  of  the  mouldings  should  be 
recognized.  In  all  these  cases,  too,  it  is  important,  as 
intimated  on  page  164,  that,  while  the  alternating  meas- 
urements seem  alike,  the  intervening  ones  should  seem 
sufficiently  unlike  the  others  not  to  confuse  the  mind  by 
suggesting  likeness  where  it  is  not  intended  to  be  sug- 
gested. 

Consonance  (see  page  3)  results  from  likeness  or  repeti- 
tion in  the  general  principles  of  construction,  rather  than 
— -though  it  involves  more  or  less  of  this — in  the  par- 
ticular details  of  form.  The  choir  of  Ely  Cathedral,  for 
instance,  Fig.  30,  page  55,  is  consonant  throughout.  So 
are  the  towers  of  St.  Stephen’s,  Caen,  Fig.  11,  page  37. 
So  are  the  roofs  and  turrets  in  Fig.  28,  page  53.  But 
in  Fig.  27,  page  51,  the  different  shapes  of  the  gables, 
window-caps,  and  turrets  of  the  roof  are  not  consonant. 
Neither  are  the  pediments  over  the  third  storeys  in  the 
towers  in  St.  Sulpice,  Fig.  82,  page  157.  The  only  thing 
that  could  excuse  these  pediments  would  be  a pediment 
over  the  central  nave.  Of  course,  in  Fig.  85,  page  163,  there 
are  many  features  that  are  not  consonant.  The  facade  of 
the  Grand  Opera  House,  Paris,  Fig.  86,  page  167,  would  be 
more  consonant  if  the  lintels  over  the  windows  behind  the 
colonnade  of  the  second  storey  surmounted  arches- corre- 
sponding to  the  arched  openings  of  the  lower  storey,  as  well 
as  to  the  rounded  roofs  at  either  end  of  this  colonnade. 

To  defer/  for  a moment,  our  consideration  of  conso- 
nance as  applied  to  architectural  measurements,  let  us 
notice  that  architectural  interchange  in  form  is  a variation 
of  consonance  in  accordance  with  which  different  sets  of 
forms,  all  the  members  of  each  of  which  sets  are  alike, 


ARCHITECTURAL  INTERCHANGE.  1 67 

are  introduced  into  different  parts  of  the  building.  Thus, 
in  this  Opera  House,  at  Paris,  Fig.  86,  the  round  arches 
over  the  entrances  of  the  lower  storey,  and  the  rounded 
outlines  over  the  sides  of  the  colonnade,  and  in  the  dome 


FIQ.  86.— OPERA  HOUSE,  PARIS. 

See  pages  15,  166,  167,  170,  175,  226. 


seen  against  the  upper  pediment,  interchange  with  the 
horizontal  lines  over  the  colonnade,  as  well  as  with  the 
windows  behind  it,  and  the  panels  in  the  storey  above  the 
colonnade. 

A unique  attempt  to  produce  effects  of  interchange 
may  be  noticed  in  the  fagade  of  St.  Etienne  du  Mont, 


PROPORTION  AND  HARMONY. 


1 68 

Paris,  Fig.  87,  page  169.  In  connection  with  almost  all 
the  openings  there  is  a combination  of  horizontal,  angular, 
and  curved  effects.  All  three  doors  have  horizontal  lin- 
tels. But  over  the  central  one  is  first  a curved  cap,  and 
above  this  a large  angular  pediment-shaped  cap.  Over  the 
doors  at  the  sides,  however,  are  first  angular  caps  and 
above  them  small  curved  caps.  All  the  windows  are 
either  rectangular  or  curved ; but  those  that  are  rect- 
angular have  curved  forms  inside  of  them.  Above  the 
large  pediment  over  the  central  entrance  is  a rounded  cap 
over  a circular  window,  and  above  this  a smaller  rect- 
angular blank  window,  enclosing  a circular  one,  and  above 
the  whole  is  a sharply  angular  gable  in  front  of  the  roof. 
Possibly  if  the  large  rounded  cap  over  the  central  front 
round  window  had  been  lower  down,  i.  e.y  just  above 
the  central  entrance,  and  if  the  pediment-shaped  cap 
which  is  just  over  this  entrance  had  been  higher  up,  i.  e., 
above  the  round  window,  and  if  the  gable  in  front  of  the 
roof  had  corresponded  or  very  nearly  corresponded  in 
shape  to  this  pediment-shaped  cap,  there  might  have  been 
some  suggestion  of  logic  in  the  arrangement,  inasmuch  as 
there  would  have  been  a gradual  increase  of  pitch  in  the 
forms  from  the  lowest  upward.  (See  “ The  Genesis  of 
Art-Form,”  pp.  291-295).  But  the  front,  as  it  is,  merely 
shows  the  method  of  interchange  run  mad. 

As  applied  to  measurements,  consonance  and  interchange , 
respectively,  are  merely  less  regular  forms  of  repetition  and 
alternation.  Every  Greek  temple  (Figs.  10,  page  36,  and 
80,  page  153)  manifests  alternation  in  the  measurements 
of  pillars  and  spaces  and  also  of  triglyphs  and  spaces, 
or  sometimes  metopes,  in  the  frieze  (Fig.  3,  page  12),  but 
it  also  suggests  interchange , there  being  a tendency  to- 
ward the  same  height  in  the  foundation,  the  entablature, 


FIG.  87.— ST.  ETIENNE  DU  MONT. 
See  pages  167,  168. 


169 


I/O 


PROPORTION  AND  HARMONY. 


and  the  tympanum  (Figs,  io,  page  36,  and  94,  page  183), 
while  the  pillars  are  much  higher  than  these,  though  usu- 
ally sustaining  to  them,  as  we  shall  find,  an  apparent  pro- 
portional relationship.  In  St.  Stephen’s,  Caen  (Fig.  11, 
page  37),  all  the  storeys  are  of  the  same  height  except 
the  lowest  storey  of  all  and  the  highest  storey  of  the  square 
part  of  the  tower,  the  storey  out  of  which  the  spires  seem 
to  spring.  This  lowest  storey  and  the  highest  storey  of 
the  square  part  of  the  tower  seem  to  agree  in  height. 

The  Opera  House  in  Paris,  Fig.  86,  page  167,  gives  us 
some  unusual  illustrations  of  interchange  as  well  as  of 
complexity  and,  one  might  say,  of  complication  in  measure- 
ments. Its  whole  height  seems  easily  divisible  into  four 
parts,  the  lowest  division  of  which  extends  above  the 
base  of  the  pillars  of  the  second  storey  as  far  as  to  the 
railing  of  its  balcony.  Looked  at  thus,  the  height 
from  the  lower  arches  to  this  railing  is  the  same  as  that 
between  the  tops  of  the  windows  of  the  second  storey 
and  the  bottom  of  the  cornice  above  them  ; the  same,  too, 
as  the  rounded  ornamental  front  above  the  pillars  at 
either  side  of  the  building,  and  also  the  same  as  a clearly 
defined  space  between  the  top  of  the  cornice  over  the 
pillars  and  the  bottom  of  the  ornamental  cornice  above 
this.  If,  however,  we  take  the  second  storey  to  be  the 
most  prominent  in  the  building,  and  therefore  consider 
the  entire  height  of  its  pillars,  which  is  evidently  the  rep- 
resentative intention,  then  between  the  arches  below  the 
pillars  and  the  bases  of  the  pillars  we  find  a height 
exactly  equal  to  that  of  the  cornice  above  the  pillars,  and 
also  of  the  ornamental  cornice  some  distance  above  this, 
and,  once  more,  of  the  rounded  cornice  over  the  dome 
seen  just  under  the  central  pediment.  Added  to  this, 
notice  the  rounded  outlines  over  each  end  of  the  row  of 


ARCHITECTURAL  INTERCHANGE. 


i;i 


pillars  on  the  second  storey.  By  placing  a finger  over  each 
of  these  rounded  ends,  one  can  recog- 
nize how  much  they  assist  the  effect  of 
the  dome  seen  against  the  pediment  in 
the  centre  by  way  of  balance ; and  also 
how  they  serve  to  connect  this  dome- 
form  and  the  rounded  arches  over  the 
entrances  of  the  lower 
floor  by  way  of  inter- 
change. This  front  would 
have  been  more  successful 
perhaps  if  these  rounded 
pediments  at  either  side 
of  the  second  storey  had 
been  half  domes  corre- 
sponding to  the  part  seen 
of  the  large  dome  of  the 
building,  or  if  the  window- 
caps  between  the  pillars 
of  the  colonnade  on  the 
second  floor  had  sug- 
gested a correspondence 
in  shape  to  the  arrange- 
ments over  the  four  pil- 
lars at  either  side  of  the 
fig.  88.  colonnade.  Nevertheless, 
kuttenberg.  as  the  building  stands,  It 
See  page  172.  is  an  admirable  example 
of  successful  proportions 
manifesting  great  variety , complexity,  fig.  89—  steeple  of  bow 
and  even  complication  of  design,  and  church,  London. 


yet  great  apparent  simplicity. 


See  page  172. 


Gradation , as  applied  to  forms,  causes  likeness  in  de- 


172 


PROPORTION  AND  HARMONY 


grees  of  difference.  As  applied  to  measurements,  of 
course,  it  would  give  likeness  in  degrees  of  these.  Figs. 


FIG.  90.— STREET  AND  BELFRY  AT  GHENT. 
See  page  172. 


88  and  89,  page  171,  Fig.  90,  and  Fig.  91,  page  173, 
all  illustrate  gradation  both  in  forms  and  measurements. 
The  regularity  with  which  the  diminution  of  size  takes 


ARCHITECTURAL  BALANCE. 


173 


place  in  each  could  evidently  not  be  produced  except 
as  a result  of  a regular 
ratio  of  diminution. 

Compare  the  tower 
in  Fig.  91,  with  the 
unsatisfactory  effect 
produced  by  a disre- 
gard of  gradation  in 
Fig.  92,  page  174,  and 
the  connection  be- 
tween gradation  in 
the  form  and  grada- 
tion in  the  propor- 
tions will  be  at  once 
apparent. 

In  the  chart  on  page 
3 of  this  volume,  com- 
plement and  balance 
are  represented  as  art- 
methods  of  earlier  de- 
velopment than  the 
others  that  we  have 
here  considered.  But 
this  is  true  only  as 
related  to  theoretical 
requirements.  Prac- 
tically, as  used  in  art, 
these  methods  may  be 
applied  not  at  the  be- 
ginning of  production, 


but  at  its  end,  in  order 

, , . , FIG.  91.— TOWER  OF  BORIS  KREMLIN 

to  complete  the  form.  Moscow. 

When  thus  used,  it  See  pages  iy2)  I?3> 


174 


PROPORTION  AND  HARMONY. 


will  be  noticed  that,  in  a sense,  balance  is  merely  alterna- 
tion containing  three  factors,  the  first  and  third  of  which 
are  alike,  and  the  second,  or  middle  one,  different.  In 


FIG.  92.  — DOME  OF  CHIAVAVALLE,  IN  ITALY 
See  page  173. 

the  human  form,  the  trunk  is  the  middle  factor,  and 
the  arms  and  legs  balance.  So,  in  the  primitive  art-form 
in  Fig.  6,  page  33,  there  is  a central  part,  and  the  equal 


ARCHITECTURAL  BALANCE. 


175 


shelves  arranged  on  either  side  of  it  balance.  In  Figs. 
11,  page  37;  12,  page  38;  81,  page  155  ; and  82,  page  156; 
the  nave  is  central  and  the  two  towers  balance.  Even  in 
Figs.  10,  page  36;  76,  page  147;  77,  page  150;  80,  page 
153  ; and  86,  page  167,  we  can  detect  a central  part  distin- 
guished, if  not  by  a pediment  or  tower,  at  least  by  having 
like  spaces  at  each  side.  The  balance  suggested  in  Fig.  86 
by  the  two  round-arched  coverings  at  each  side  of  the 
colonnade,  corresponding  with  each  other  and — though 
only  in  a much  broader  sense — with  the  dome  seen  rest- 
ing against  the  upper  pediment,  has  already  been  noticed. 
Now  in  the  arch  in  Fig.  78,  page  152,  observe  the  high 
central  opening  and  the  two  balancing  openings  at 
each  side  of  it.  All  the  proportions  of  this  arch,  too,  will 
bear  study.  The  perpendicular  sides  of  the  small  open- 
ings are  to  those  of  the  large  central  opening  as  2 : 3.  So, 
too,  is  the  horizontal  distance  between  the  pillars  at  each 
side  of  the  small  openings  and  between  the  pillars  at 
each  side  of  the  large  central  opening.  The  height  of  the 
space  between  the  pillars  at  each  side  is  divided  horizon- 
tally into  three  equal  parts,  the  lowest  extending  to  the 
tops  of  the  large  bases  of  the  pillars,  and  the  second  to 
the  tops  of  the  horizontal  ornamentation  above  the  small 
arches.  The  distance  from  the  top  of  the  large  central 
arch  to  the  top  of  the  upper  cornice  is  the  same  as  that 
between  the  pillars  that  are  each  side  of  the  central  arch; 
and  the  height  of  the  panel,  exclusive  of  the  cornice,  ex- 
tending across  the  entire  top  of  the  arch  is  the  same  as 
the  height  of  the  inclosed  space  above  each  of  the  small 
arches  at  the  sides.  As  has  been  said  before,  the  arch  is 
not  square,  though  owing  to  the  effect  of  the  vertical  lines 
of  the  pillars  it  seems  to  be  so.  At  the  same  time,  the 
breadth  of  the  arch,  as  measured  from  the  outside  lines 


176 


PROPORTION  AND  HARMONY. 


of  the  outside  pillars  alone,  is  the  same  as  its  height.  It 
is  partly  for  this  reason  that  though,  when  looked  at  in 
one  way,  it  is  not  square,  when  looked  at  in  another  way 
it  is  square,  and  when  looked  at  in  any  way  it  appears  to 
be  square. 

From  all  that  has  been  said  in  this  chapter  it  is  appar- 
ent that  we  can  draw  the  same  conclusion  here  as  was 
drawn  from  our  review  of  proportion  as  manifested  in  the 
human  form,  namely,  that  while  it  necessarily  involves 
the  use  of  such  ratios  as  1 : 2,  2 : 3,  3 : 4,  4 : 5,  etc.,  it  never- 
theless, fundamentally  considered,  is  no  more  than  an  ap- 
plication to  measurements  and,  as  connected  with  these, 
to  spaces  of  the  same  methods  of  art  which  are  indicated 
in  the  chart  on  page  3,  and,  as  applied  in  all  the  arts,  are 
described  in  a general  way  in  “ The  Genesis  of  Art-Form.” 


CHAPTER  XI. 


PROPORTION  IN  GREEK  ARCHITECTURE. 

Greeks  Pre-eminent  in  Architecture — The  Secret  of  their  Methods  of  Pro- 
portion Involves  more  than  the  Study  of  Measurements — The  Mind  is 
Conscious  of  Ratios  in  Proportion — -It  has  Reasons  for  Using  them — 
The  Reasons  of  the  Greeks  may  have  been  Different  from  what  we 
Suppose — To  Understand  the  Reasons  we  must  Judge  their  Buildings 
as  we  do  Other  Art-Products,  by  their  General  Effects — And  Draw  our 
Conclusions  from  Many  Specimens — The  Authorities  Consulted  in  the 
Measurements  to  be  Quoted  in  this  Book — The  Greek  Temple  Com- 
posed of  Different  Sets  of  Factors,  each  Set  Having  the  Same  Measure- 
ments— To  Show  this  we  are  to  Start  with  Factors  of  Small  Dimensions 
— Same  Height  in  the  Abacus  and  Corona  of  Horizontal  and  Raking 
Cornices,  the  Ovolo,  Cyma  Recta,  etc. — Measurements  of  these  Parts 
in  Different  Temples — Variations  and  Explanations — Like  Proportions 
of  all  the  Parts  just  Mentioned  to  the  Height  of  the  Capitals,  and  of 
both  the  Cornices  and  the  Steps — Ratios  of  I : 2 Sustaining  this  State- 
ment— Of  i : 3 — Of  2 : 3 — Like  Ratios  of  the  Parts  just  Mentioned  to 
the  Height  of  the  Architrave,  Frieze,  and  Raking  Cornice  with  Cyma- 
tium — Also  to  Upper  Diameter  of  Shafts  and  Width  of  Metopes — Ex- 
planations— Ratios  of  1 : 2 — Of  1 : 3 — Remarks — Like  Ratios  of  the 
Parts  just  Mentioned  to  the  Height  of  the  Entablature,  Tympanum, 
and  Width  of  Upper  Inter-Columnation — Confirmation — Insufficiency 
of  Data  with  Reference  to  the  Tympanum  and  Pediment — Like  Ratios 
of  the  Height  of  Entablature  and  Pediment  Spaces,  Differently  Divided, 
to  the  Height  of  Column-Space — The  Different  Methods  of  Dividing 
these  Gave  Opportunity  for  Originality  Exercised  in  Conformity  to 
Law. 

w HEN  speaking  of  the  human  figure  it  was  said  that 
of  all  artists  who  have  ever  studied  its  proportions 
the  Greeks  are  acknowledged  to  have  known  most  about 
them.  The  same  is  true  with  reference  to  architectural 


177 


i ;8 


PROPORTION  AND  HARMONY. 


proportions.  This  subject  of  proportion  in  all  its  appli- 
cations is  supposed  to  have  been  mastered  by  them 
as  by  no  other  people  ; and  almost  all  the  works  written 
upon  it  in  modern  times  that  are  of  value  have  been 
attempts  to  prove  that  the  writer  has  at  last  discovered 
the  clew  to  the  methods  of  measurement  exemplified 
in  the  masterpieces  on  the  Acropolis,  where,  as  Lloyd 
tells  us  in  the  appendix  to  Cockerill’s  “Temples  of 
/Egina  and  Bassae,”  page  68,  “ architectural  elements 
combine  with  the  harmonious  flow  of  the  poetry  of  Soph- 
ocles, and  with  a coherence  and  cogency  that  are  truly 
Demosthenic,”  comparing  “with  some  of  the  great  works 
of  classic  music  in  which  the  genius  of  the  composer 
has  only  to  contend  against  his  matchless  command  of 
the  scientific  resources  of  his  art.”  It  seems  desirable, 
therefore,  before  leaving  this  subject,  to  find  out  whether, 
in  any  degree,  the  principles  that  have  been  unfolded 
are  sufficient  to  account  for  the  measurements  under- 
lying  the  proportions  of  the  Greek  temples,  which  so 
many  admire,  but  apparently  without  knowing  why  they 
do  so. 

In  order  to  accomplish  our  object,  it  is  necessary  to  be- 
gin by  recalling  the  line  of  thought  in  Chapter  IV.,  and 
to  recognize  again  that  it  is  impossible  to  solve  the  se- 
crets of  the  Greek  proportions  by  studying  accurately 
merely  the  measurements  of  their  buildings.  It  is  only 
in  a very  slight  degree  that  we  are  made  wiser  for  practi- 
cal architectural  work  when  we  have  learned  that  in  the 
Parthenon  the  width  of  the  column  was  to  that  of  the 
whole  breadth  of  the  front  as  5 : 81,  or  that  the  “ height 
was  to  the  breadth  as  9:  14.” 

As  has  been  said,  proportion  is  not  the  analogue  of  mu- 
sical harmony.  Therefore  the  mind  cannot,  as  from  har- 


GREEK  ARCHITECTURAL  PROPORTIONS. 


1 79 


mony,  experience  the  effects  of  ratios  aside  from  being 
conscious  that  they  exist.  The  analogue  of  proportion  is 
rhythm  ; and  in  this,  though  one  may  do  no  counting,  he 
knows  that  he  could  do  it,  if  he  chose,  and  with  satisfactory 
results.  He  evidently  could  not  know  this  if  confronted 
with  the  effects  of  any  such  ratios  as  5 : 81  or  9 : 14.  Nor, 
even  though  the  ratios  be  expressible  in  comparatively 
small  numbers,  can  one  be  sure  that  by  knowing  merely 
these  he  can  know  all  that  is  to  be  learned  about  proportion 
as  it  was  developed  by  the  Greeks.  “ I believe,”  says  the 
Greek  scholar,  “in  using  the  proportion  7:12  or  9:14 
because  the  Greeks  used  it.”  This  kind  of  an  argument 
may  do  for  a pedagogic  Hellenist,  but  it  will  not  do  for  a 
practical  architect.  If  the  Greeks  used  this,  or  any  other 
proportion,  they  had  a reason  for  doing  it.  If  the  archi- 
tect of  our  day  use  it  without  knowing  this  reason,  he  will 
use  it  irrationally,  and  very  likely  erroneously.  If,  for  in- 
stance, the  breadth  of  a hall  be  to  its  length  as  7 : 12,  and 
it  have  an  altar  or  columns  or  heavy  doorways  at  one  or 
both  ends,  it  is  possible  that  the  proportions  may  look 
like  6:  12.  As  has  been  shown  to  an  extent,  and  will  be 
shown  more  clearly  in  Chapters  XIII.  to  XV.,  there  were 
many  of  the  dimensions  which  the  modern  Hellenist 
would  follow  slavishly,  which  the  Greeks  used  on  account 
not  of  what  they  were,  but  of  what  they  appeared  to  be. 
Nor,  even  admitting  that  the  proportions  were  used  on 
account  of  what  they  were,  is  it  certain  that  the  parts  of 
the  buildings  which  modern  students  suppose  these  pro- 
portions to  determine  are  the  parts  which  the  Greeks  in- 
tended them  to  determine.  When,  for  example,  the 
height  of  a temple,  pediment  included,  is  to  its  breadth 
as  7 : 12,  or  9 : 14,  is  this  ratio  the  cause  of  these  dimensions, 
or  only  an  incidental  and,  therefore,  almost  accidental  re- 


i8o 


PROPORTION  AND  HARMONY. 


suit  of  arrangements  for  which  the  cause  is  to  be  sought 
elsewhere, — for  instance,  in  a desire  to  make  the  entabla- 
ture and  pediment  appear  of  the  same  height,  and  both 
together  to  appear  to  sustain  a certain  ratio  to  the  col- 
umnar space  below  them  ? See  what  is  said  of  Cologne 
Cathedral  on  pages  1 53  to  1 55.  In  any  view  of  the  subject, 
it  is  surmisable,  at  least,  that  the  consideration  which  mod- 
ern students  pay  to  an  accidental  result  may  overlook  an 
essential  cause,  which  alone  can  enable  one  to  interpret 
the  proportion  rationally.  Whatever  benefit  we  may  de- 
rive, therefore,  and  it  may  be  much,  from  the  accurate 
measurements  of  the  buildings  of  the  Greeks,  we  can 
never  find  out,  in  this  wa)^  alone,  those  elements  of  pro- 
portion which  they  esteemed  of  most  importance. 

To  understand  what  these  elements  were  we  must  ex- 
amine their  buildings,  as  intimated  on  page  35,  not  near  at 
hand,  but  from  a distance.  The  same  holds  good  in  prin- 
ciple as  applied  to  the  processes  through  which  we  come 
to  understand  any  works  of  art.  If  we  wish  to  study 
Raphael,  we  do  not  start  by  trying  to  detect  the  way  in 
which  he  put  the  paint  upon  his  canvas.  We  sit  before  a 
finished  work  of  his  where  we  can  gaze,  unconscious  of 
the  paint,  at  what  seems  flesh  and  blood  infused  with 
thought  and  grace  and  beauty.  We  feel  his  composition 
in  our  souls  before  we  touch  it  with  our  fingers.  If  we 
wish  to  study  Shakspere,  we  do  not  start  by  testing  how 
his  lines  will  parse  and  scan.  We  read,  or  we  hear  read, 
an  act  or  a scene.  We  listen  to  the  music  of  his  sentences. 
We  heed  the  accents  of  the  living  men  of  his  drama.  We 
note  the  play  of  fancy  that  passes  between  them,  their 
bursts  of  passion  and  the  friction  of  their  thoughts  as  they 
flame  out  so  that  heaven  and  hell  both  brighten  to  reveal 
their  secrets.  We  move  with  ordinary  men  and  women, 


GREEK  ARCHITECTURAL  PROPORTIONS.  l8l 

but  cast  in  an  heroic  mould.  We  live  in  history  that  was 
dead  but  has  found  a resurrection.  We  revel  in  the  bliss  of 
a new  world  that  the  poet’s  genius  has  created.  These 
are  facts  that  pedants  never  seem  to  realize.  They  teach 
the  spelling-book  and  mathematics,  and  think  that  out 
of  these  the  works  of  art  develop.  But  works  of  art  are 
germed  in  seed  that  drops  down  from  above.  Like  Min- 
erva from  the  brain  of  Jove,  they  spring  to  life  full-armed  ; 
and  soar  through  air  before  they  tread  the  earth ; and 
when,  through  using  spelling-books  and  mathematics, 
men  make  the  art-forms  fit  intelligence,  these  forms  have 
no  artistic  value  save  to  those  who  know  enough  to  search 
beneath  them  for  the  principle  that  formed  them,  a prin- 
ciple manifested  in  results  that  cannot  be  perceptible  ex- 
cept to  larger  and  more  comprehensive  views  in  which  the 
parts  appear  related  to  the  wholes,  and  the  wholes  related 
to  the  parts.  So,  to  judge  of  these  Greek  buildings,  we 
must  see  them  from  a distance  where  such  views  are  possi- 
ble. Indeed,  the  very  conception  that  the  Greek  had  of 
proportion  indicates  as  much.  How  could  he  study  what 
he  considered  the  intermeasurement  between  the  parts, 
except  from  a point  where  all,  or  at  least  a majority  of  all, 
the  parts  were  visible? 

Again,  in  order  to  find  what  the  Greeks  considered  de- 
sirable in  architectural  proportion,  we  should  draw  our 
conclusions  from  examining  as  many  temples  as  we  can. 
The  results  to  be  given  here  have  been  compiled  from 
the  measurements  of  almost  every  ancient  Doric  temple 
in  existence,  as  these  are  variously  indicated  in  Pen- 
rose’s “ Principles  of  Athenian  Architecture,”  Cockerill’s 
“Temples  of  Afgina  and  Bassae,”  Stuart’s  “Antiquities 
of  Athens,”  and  the  summaries  made  of  the  results  of 
the  labors  of  such  men  as  Delagardetta,  Ross,  Shaubert, 


182 


PROPORTION  AND  HARMONY. 


Hansen,  and  Blouet,  in  Hittorf’s  “ Architecture  Antique 
de  la  Sicile.”  The  figures  to  be  used  are  the  same  as  in 
these  works.  By  consequence,  as  can  easily  be  deter- 
mined, they  sometimes  represent  feet  and  decimals  of 
feet,  sometimes  relative  measurements  of  a given  standard, 


FIG.  93.— COLUMN  AND  ENTABLATURE 
OF  TEMPLE  OF  /EGINA. 

See  pages  183,  185,  187,  188,  191,  192,  203,  219. 


and  sometimes  follow  the  French  system.  But  as  meas- 
urements of  the  same  temple  are  always  indicated  accord- 
ing to  the  same  system,  and  as  it  is  necessary  for  us 
to  observe  merely  the  relationships  between  these,  the 
results,  as  represented  in  the  figures  used  in  each  of  these 
works,  will  answer  our  purposes.  The  initial  letters  of 
the  authorities  already  mentioned,  P.,  C.,  S.,  and  H.,  with 


GREEK  ARCHITECTURAL  PROPORTIONS. 


183 


L.  for  Lloyd’s  appendix  to  the  works  of  Penrose  and 
Cockerill,  will  indicate  sufficiently  the  sources  of  the 
measurements.  It  is  to  be  understood,  too  that  in  many 
cases  no  measurements  of  the  parts  that  we  wish  to  com- 
pare are  given,  the  measurers  not  deeming  them  of  im- 
portance, or  the  temple  being  in  ruins.  Especially  do  we 
find  lacking  the  measurements  of  the  corona  and  the 


FIG.  94.— GREEK  DORIC  TEMPLE  OF  -CGINA. 

See  pages  42,  170,  183,  185-189,  191,  192,  196,  197,  204,  207,  224. 


cyma  recta  of  the  cornices,  both  horizontal  and  raking 
(see  Fig.  93,  page  182,  and  Fig.  94),  and  of  the  cyma- 
tium,  or  pedimental  moulding,  over  the  raking  cornice. 
This  is  unfortunate  for  several  reasons,  chiefly  because, 
as  we  shall  find,  the  dividing  line  between  the  space  occu- 
pied by  the  entablature  and  the  pediment  was  not  infre- 
quently below  the  upper  mouldings  of  the  cornice  ; and 
the  cymatium  needs  to  be  included  with  the  pediment  be- 
fore one  can  make  out  the  latter’s  exact  relationship  to 


1 84  PROPORTION  AND  HARMONY. 

the  rectangle  of  the  entablature  beneath.  But  it  is  hoped 
enough  is  known  to  justify  the  conclusions  that  will  here 
be  reached. 

It  seems  strange  that  any  who  have  undertaken  to 
unravel  the  mysteries  of  Greek  proportion  should  have 
failed  to  begin  by  recognizing  the  most  apparent  fact 
with  reference  to  it.  Yet,  notwithstanding  the  rows  of 
like  columns  and  of  like  equal  horizontal  divisions  in  the  en- 
tablatures, which  stare  every  one  in  the  face  the-paoment 
that  a Greek  temple  is  seen,  many  havte  apparently  failed 
to  notice  that  the  whole  is  composed  of  different  sets  of 
factors,  all  the  members  of  each  set  of  which  are  intended 
to  appear  to  have  the  same  measurements.  Of  course,  if 
what  has  been  said  thus  far  in  this  discussion  be  true, 
each  of  these  measurements  represents  what  in  rhythm 
would  be  a note  or  bar  of  the  same  length;  and  it  was  by 
combining  these  notes  or  bars  with  others  in  proportion 
to  them,  that  the  Greek  built  up  his  architectural  rhythm. 
What  though,  as  tested  by  plummet  and  line,  some  of 
these  measurements  that  seem  to  be  exactly  alike  do  not 
prove  to  be  so  ? There  are  reasons  for  this,  which  will 
be  explained  in  Chapters  XIII.  to  XV.  At  present,  it 
is  enough  to  recall  that  such  discrepancies  are  in  anal- 
ogy with  facts  exemplified  in  all  the  arts.  If  slight 
enough  to  escape  easy  detection,  differences  in  things 
supposed  to  be  alike  are  always  allowable.  In  musical 
rhythm,  the  first  of  three  equal  notes  beginning  a bar, 
owing  to  its  accent,  is  allowed  a longer  time  than  the 
other  two.  In  harmony  produced  by  instruments  tuned 
according  to  the  present  temperate  scale,  the  chords  used 
do  not  represent  with  absolute  accuracy  the  partial  tones 
composing  their  separate  notes.  In  poetry,  successive 
lines  ending  in  words  like  laud  and  God , are  accepted  as 


GREEK  ARCHITECTURAL  PROPORTIONS. 


I85 


substitutes  for  rhymes  ; and  in  painting,  colors  that  fail, 
and  yet  just  fail,  to  form  perfect  complements,  are  some- 
times used  for  them.  Why  should  it  not  be  the  same  in 
architecture  ? 

In  examining  these  sets  of  measurements  in  the  Greek 
temples,  it  will  be  convenient,  as  well  as  logical,  to  take 
up  first  the  parts  that  are  comparatively  smaller,  and  then 
those  that  are  larger.  Of  the  smaller  parts  again,  some, 
like  those  in  many  of  the  mouldings  or  fillets,  are  so  ap- 
parently alike  that  even  if  their  exact  measurements  could 
be  ascertained,  which  is  not  the  case,  we  should  not  need 
to  consider  them  here.  In  mentioning  other  sets  of 
members,  in  order  to  be  able  to  refer  to  them  readily 
when  speaking  of  them  later,  they  will  be  put  into  classes 
designated  by  Roman  letters,  thus,  I.,  II.,  III.,  etc. 

I.  We  shall  start  with  small  enough  numbers,  if  we 
compare  first  (see  Fig.  93,  page  182)  the  abacus , i.  e.,  the 
square  flat  stone  at  the  top  of  the  capital  of  the  column, 
with  the  corona,  or  flat  stone  forming  the  lowest  projection 
of  the  horizontal  cornice  over  the  entablature,  and  also  with 
the  corresponding  lowest  projection  of  the  raking  cornice 
forming  the  angle  over  the  pediment.  (See  Fig.  94,  page 
183.)  These  three  were  usually  of  the  same  apparent 
height,  and  the  similar  flatness  and  plainness  of  the  three 
emphasize  their  likeness.  They  were  usually  also  of 
proportions  that  make  them  seem  of  the  same  height 
as  the  ovolo  (Fig.  93,  page  182),  i.  e.,  the  rounded  part 
of  the  column’s  capital  immediately  under  the  abacus,  and 
also,  at  times,  to  seem  of  the  same  height  as  the  united 
mouldings  at  the  top  of  the  architrave  or  of  the  frieze,  as 
well  as  of  the  cyma  recta,  i.  e.,  the  partly  rounded  mould- 
ing of  both  the  horizontal  cornice  and  of  the  raking 
cornice  (Fig.  94,  page  183)  immediately  over  the  corona 


1 86  PROPORTION  AND  HARMONY. 

of  each.  Here  are  three  and,  at  times,  more  members  of 
like  height.  Occasionally,  exactly  six  of  these,  three  that 
are  flat  and  three  adjoining  them,  respectively,  that  are 
curved,  are  of  like  height.  Now  for  our  proofs.  In  the 
temple  of  Hvgina(Fig.  94,  page  183),  the  height  of  the  abac- 
us (C.,  T.  at  vEg.,  pi.  7)  is7"65o;  corona  of  cornice,  7"666; 
that  of  the  raking  cornice  is  not  given  but  is  apparently  the 


FIG.  95.  — RESTORATION  OF  THE  WEST  END  OF  THE  ACROPOLIS,  ATHENS. 

See  pages  186,  190,  210,  211,  216,  2:9,  252,  257. 

same ; ovolo  of  capital,  not  to  the  rings,  but  to  the  point 
where  it  swells  out  from  the  upper  diameters  of  the 
column  (estimated),  j"6  ; moulding  over  architrave,  7'/3-|-. 
Temple  of  Phigaleia  (C.,  pi.  6),  abacus,  j"  125  ; corona  of 
cornice,  6"g  ; of  raking  cornice,  apparently  the  same ; ovolo, 
7- \-  (estimated) ; mouldings  over  architrave,  6"975  ; over 
frieze,  6"66o.  Propylsea,  the  central  building  in  Fig.  95, 
above  (P.,  pi.  13),  abacus,  .96;  corona  of  horizontal 
cornice,  .882;  of  raking  cornice,  .751,  but  the  latter  has 
mouldings  not  included  in  this.  Parthenon  (Fig.  96, 


GREEK  ARCHITECTURAL  PROPORTIONS.  1 87 

page  190)  (P.,  sec.  2 and  appendix),  abacus,  1.149;  co- 
rona of  cornice  over  entablature,  probably  including,  as 
it  need  not,  the  fillet,  1.302;  of  the  raking  cornice,  1.174. 
In  the  temples  in  Hittorf’s  summary,  the  dimensions  of 
the  corona  are  not  given  ; but  to  one  recalling  what  has 
been  said,  namely,  that  the  abacus  is  usually  of  the  same 
height  as  the  ovolo,  and  half  that  of  the  cornice,  it  is  evi- 
dent that  the  following  indicate  the  same  apparent  pro- 
portions as  those  already  noticed  : 


Abacus. 

Whole  Cap. 
to  Rings  be- 
low Ovolo. 

Cornice. 

Nemesis  at  Rhamnus 

0.131 

0.251 

0.212 

Themis  at  Rhamnus 

0.158 

0.308 

0.310 

At  Sunium  ..... 

o.ig6 

0.376 

0.390 

Ceres  at  Eleusis  .... 

0.329 

0.562 

0.567 

Neptune  at  Psestum  .... 

0.432 

0.882 

0.797 

The  Theseum  ..... 

0.199 

0.396 

0.346 

Concord  at  Agrigentum 

0.320 

0.669 

0.615 

Juno  Lucina  at  Agrigentum 

0.445 

1. 013 

1.034 

R.  at  Selinus  ..... 

0.508 

1.063 

1. 031 

In  some  other  cases  the  ovolo,  as  measured,  seems 
higher  than  the  abacus  ; but  this  result  is  probably  pro- 
duced, as  in  the  temple  of  Phigaleia,  by  the  fact  that  the 
rings  or  fillets  are  some  inches  below  the  place  where  the 
ovolo  swells  out  from  the  column,  and  therefore  (see 
page  182)  below  where  the  effect  begins  that  we  wish  to 
compare  with  the  abacus.  (See  Figs.  93,  page  182,  and 
94,  page  183.)  In  other  cases,  the  likeness  in  height 
between  the  abacus  and  the  corona  of  the  cornice  is  not 
indicated  quite  so  distinctly.  But  we  must  remember 
that  the  entablature  contained  many  mouldings  or  fillets, 
and  of  the  measurements  that  we  have  some  are  made 
to  include  one  of  these  and  some  another.  There  is  no 
temple  in  Hittorf’s  summary  that  seems  more  out  of  the 
way  than  that  of  Phigaleia.  Yet  the  detailed  measure- 


I 88  PROPORTION  AND  HARMONY. 

ments  of  this,  as  made  by  Cockerill  and  quoted  from  him 
on  page  186,  sufficiently  prove  our  ground.  As  given  by 
Hittorf,  they  are  as  follows:  abacus,  0.178;  capital  to 
below  ovolo,  0.409 ; cornice,  0.284.  All  that  we  wish  to 
show  now  is  that  the  abacus  and  coronae  of  the  cornices 
were,  as  a rule,  of  the  same  appareiit  height,  and  that, 
usually,  the  same  was  true  of  the  other  members  that 
have  been  mentioned  ; and  it  may  be  said  that  there  is 
nothing  in  the  known  divisions  of  any  temples  that  dis- 
proves this  rule,  although  some  furnish  no  evidence  either 
for  it  or  against  it.  However,  if  the  reader  wish  to  ex- 
amine this  subject  for  himself,  the  measurements  given 
under  the  next  heading  (II.)  will  enable  him  to  do  so. 

II.  The  height  of  each  of  the  six  members  just  con- 
sidered bore  a relationship  expressible  by  low  numbers — 
usually  1 : 2 or  1 : 3,  and  in  a few  cases  of  2 : 3— to  the  height 
of  each  of  three  and  sometimes  of  four  other  members, 
three  of  which  were  a combination  of  one  flat  and  of  one 
curved  member.  These  were  the  whole  horizontal  cor- 
nice, the  whole  raking  cornice  (Figs.  93,  page  182  and  94, 
page  183),  the  whole  capital  of  the  column,  and  sometimes 
the  steps  of  the  stylobate,  i.  e.,  the  foundation.  (See  Fig. 
94,  page  183,  also  Fig.  10,  page  36.)  As  has  been  intimated 
before,  the  exact  measurements  of  the  capitals  and  cor- 
nices are  sometimes  difficult  to  determine.  Both  contain 
several  mouldings  separating  them  from  other  members, 
yet  entering  into  the  general  effect ; and  the  measurers 
have  not  considered  these  mouldings.  Nevertheless, 
by  bearing  this  fact  in  mind,  their  measurements  may 
indicate  ratios  sufficiently  exact  for  our  purpose.  The 
ratios  indicating  the  relationship  between  the  abacus  or 
cornice  and  the  steps,  as  also  the  whole  foundation,  would 
vary.  In  some  temples,  but  not  in  all,  the  steps  were  for 


GREEK  ARCHITECTURAL  PROPORTIONS.  1 89 

convenience,  and  would  always  be  of  a somewhat  similar 
height.  In  a large  temple  they  might  be  as  high  as  the 
cornice  ; in  a small  one,  they  might  be  higher.  What  is  of 
importance  is  that  they  always  were  made  to  sustain  a 
certain  relationship  to  something.  It  is  well  to  observe, 
too,  that,  as  they  were  nearer  to  the  spectator  than  the 
members  above  the  column,  and  also  were  seen  on  a level, 
and  not  at  an  elevation  and  therefore  obliquely,  as  were  the 
latter,  we  should  expect,  in  accordance  with  Greek  meth- 
ods, that  to  appear  of  the  same  height  as  these  members 
they  would  sometimes  be  given  a little  different  height. 
It  seems  well  to  add  that  in  few  of  the  temples  is  the 
height  of  the  steps  or  of  the  whole  stylobate  given. 

In  confirmation  of  what  has  been  said  the  reader  may 
begin  by  noticing  the  measurements  of  the  temples  in 
Hittorf’s  summary,  mentioned  in  the  third  paragraph 
above.  In  every  one  of  these  temples  the  proportion 
between  the  abacus  and  cornice  is  1:2.  The  same  is  true 
of  the  temple  at  /Egina  (Fig.  94,  page  183)  (C.,  pi.  7),  in 
which  the  abacus  is  7"6 25,  or,  if  we  include  a slight  space 
between  it  and  the  entablature,  7"65o;  while  the  hori- 
zontal cornice,  leaving  out  the  2"8-inch  fillet  at  the  top, 
which,  if  colored  differently,  as  in  Cockerill's  plates,  would 
look  like  a dividing  line  between  cornice  and  pediment, 
measured  i,4/,665.  The  raking  cornice  seems  the  same; 
so  does  the  capital  of  the  column  including  abacus  and 
the  ovolo  to  the  point  where  it  is  no  wider  than  the  upper 
diameter  of  the  column.  And  so,  too,  does  the  top  step 
of  the  stylobate,  which  happens  to  be  given  in  this 
temple,  as  i/3"875-  In  the  Theseum  (Fig.  10,  page  36), 
in  which,  as  Hittorf’s  summary  has  shown,  the  cornice  is 
twice  the  height  of  the  abacus,  we  find,  in  a place  (P.,  pi. 
35)  where  the  height  of  the  latter  is  not  given,  that  the 


PROPORTION  AND  HARMONY. 


I90 


cornice  measures  1.090,  while  the  two  steps  of  the  founda- 
tion that  are  mentioned  measure,  respectively,  1.190  and 
1. 129. 

In  other  temples,  the  proportion  between  the  parts 
that  we  are  considering  is  1 : 3.  At  Selinus,  where  this 
method,  in  imitation  of  the  old  temple  T.,  seems  to  have 
been  common,  we  find  (H.)  : 


Abacus. 

Cap.  of  Col- 
umn to  Ring 
belowOvolo. 

Cornice. 

Temple  T. 

0.568 

1.076 

1. 618 

Temple  S.  ..... 

0.334 

0.658 

0.953 

Temple  D.  ..... 

0.359 

0.716 

I.029 

Temple  C.  ..... 

0.386 

0.716 

I.OO9 

Minerva  at  Syracuse  .... 

0.445 

1. 013 

1.407 

There  are  other  temples  in  which  these  proportions 
seem  to  have  been  intended  to  be  2 : 3.  In  that  of  Jupi- 
ter at  Olympia  (H.),  the  abacus  measures  0.420  ; from  the 


FIG.  96.— THE  PARTHENON. 

See  pages  15,  186,  igo,  201,  211. 


top  of  the  same  to 
the  rings  of  the 
capital  measures 
1.020;  while  the 
cornice  measures 
0.680.  In  the  tem- 
ple of  Phigaleia 
(C.,  pi.  6),  the  aba- 
cu  s measures 
7*125,  the  corona 
6*9,  the  cornice 
9"73,  and  the  mid- 


dle step  of  the  stylobate  9;/883.  In  the  Propylsea,  the  cen- 
tral temple  in  P'ig.  95,  page  186  (P.,  pi.  13),  the  corona  of 
the  cornice  measures  .882,  the  whole  cornice  1.316.  In 
the  Parthenon  (Fig.  96),  the  abacus  measures  1.149,  the 
whole  cornice  1.951,  and  the  upper  step  of  the  stylobate 


GREEK  ARCHITECTURAL  PROPORTIONS.  I9I 


1.814.  In  the  Temple  of  the  Giants  at  Agrigentum,  the 
abacus  measures  0.853  ancl  the  cornice  1.374.  We  have 
left  now  only  two  temples  to  which  we  have  not  applied 
these  principles.  In  that  of  Jupiter  at  Nemea,  the  abacus 
measures  0.260,  the  capital  with  the  ovolo  measures  0.475, 
and  the  cornice  0.339  ; but  in  this  temple  the  architrave  is 
given  as  1.023,  and  the  frieze,  which,  according  to  rule, 
should  be  nearly  the  same,  as  1. 140.  By  a slip  of  the  pen 
in  transcribing,  or  by  the  very  natural  mistake  of  including 
mouldings  which  should  go  with  the  cornice,  this  may 
have  been  made  I,.i40  instead  of  1.040,  which  would  make 
the  cornice  0.439,  ar*d  related  to  the  abacus  as  1 : 2.  Some 
similar  error  may  account  for  the  measurements  ascribed 
to  the  Temple  of  Diana  at  Eleusis.  Here  the  abacus  is 
0.18 1,  capital  with  ovolo  0.330,  and  cornice  0.263.  If  the 
latter  were  0.363  we  should  have  1 :2  again.  But,  admit- 
ting the  recorded  measurements  to  be  correct,  we  can  say  at 
least  that  abacus  to  cornice  in  both  these  cases  is  as  2 : 3. 

III.  Again,  the  like  height  of  each  of  the  three  mem- 
bers just  considered,  i.  e.,  of  the  two  cornices  and  of  the 
capitals,  bore  a relationship  expressible  in  low  numbers, 
usually  1:2,  1 : 3,  or  2 : 3,  to  the  like  height  of  two  other 
members,  namely,  the  architrave  and  the  frieze  (see  Fig.  93, 
page  182),  and  apparently  also,  in  the  smaller  temples,  to 
the  combined  height  of  the  raking  cornice  and  the  cyma- 
tium,  both  together  forming  the  angular  top  of  the  gable  of 
the  pediment  (see  Fig.  94,  page  183).  This  latter  statement, 
however,  cannot  be  proved,  as  almost  all  the  pediments 
are  in  ruins  and  restored  only  according  to  supposition. 

But  this  is  not  all.  These  vertical  dimensions  are  the 
same,  as  a rule,  as  the  horizontal  diameters  of  the  columns 
just  below  their  capitals,  where,  therefore,  because  nearer 
together,  the  eye  could  best  compare  the  columns,  archi- 


192 


PROPORTION  AND  HARMONY. 


trave,  and  frieze.  The  horizontal  dimensions  of  the 
metopes  (see  Fig.  3,  page  12)  of  the  frieze  also  fre- 
quently measured  the  same.  In  other  cases,  these 
metppes,  as  well  as  the  triglyphs  which  separated  them, 
seem  intended  to  appear  just  as  wide  as  the  height  of  the 
cornice,  rather  than  of  the  frieze  (see  Fig.  93,  page  182). 

In  considering  the  measurements  needed  to  sustain 
these  statements,  great  difficulty  is  experienced,  even  with 
the  drawings  before  us,  in  determining  exactly  what 
mouldings  ought  to  go  with  the  architrave,  the  frieze,  the 
cornice,  and  the  pediment — not  as  they  are  outlined  in 
modern  times,  but  as  their  builders  meant  them  to  be 
outlined.  When,  as  in  ALgina,  there  is  reason  to  think 
that  the  upper  mouldings  of  the  cornice  were  painted 
precisely  like  the  pediment,  we  infer  that  they  were  in- 
tended to  enter  into  the  effect  of  the  pediment,  and  the 
same  of  its  lower  mouldings  as  related  to  the  frieze. 
At  other  times,  certain  mouldings  between  all  these  mem- 
bers seem  to  have  been  intended  to  have  the  effect  merely 
of  dividing  lines.  If  so,  in  calculating  the  proportions, 
the  measurements  of  the  architrave,  frieze,  and  cornice 
should  be  considered  so  far  only  as  they  are  between 
these  lines.  In  the  measurements  that  we  have,  these 
facts  are  ignored.  However,  notwithstanding  all  that  can 
be  said  of  the  impossibility  of  obtaining  exact  data,  it  is 
remarkable  how  clear  the  proof  is  of  a general  intention 
to  produce  such  like  effects  as  have  been  mentioned. 

To  show  the  bearing  of  what  has  been  said,  according 
to  C.,  pi.  7,  in  the  temple  of  Aigina  (Fig.  94,  page  183)  the 
cornice  measures  i/7,/465,  the  architrave  2'g",  the  frieze 
2rQ)'  125,  and  the  upper  diameter  of  the  columns  2/5//25. 
If  from  the  cornice  we  take  the  upper  moulding  2ff8, 
which  clearly  belongs  to  the  pediment,  the  result  is 


GREEK  ARCHITECTURAL  PROPORTIONS.  193 


i'4"665,  just  half  of  with  a ratio  of  1 : 2.  Ap- 

parently, too,  the  horizontal  measurement  of  the  upper 
column  would  look  near  enough  2'g" . But  we  can  do 
better  than  this.  Treating  one  moulding  of  3"9  as  a 
dividing  line  over  the  architrave,  and  another  of  3^259 
as  a dividing  line  over  the  frieze,  we  can  make  these  mem- 
bers, respectively,  2^ 'To  and  2/5"866;  and  if  at  the  same 
time  we  treat  the  two  mouldings  2"8  and  2"  over  the 
cornice  in  the  same  way,  we  can  make  that  member 
l'2ff66$,  and  twice  of  this  is  2'5"330.  Precisely  the 
same  methods  are  pursued  in  each  case,  and  the  pro- 
portions are  almost  exact.  The  bearing  of  this  upon  the 
measurements  of  Hittorf,  in  which  these  mouldings  are 
not  noticed,  is  that  he  represents  the  measurements  of  the 
temples  thus:  architrave  0.845,  frieze  0.847,  upper  diame- 
ter of  the  column  0.733,  metopes,  0.800,  cornice  0.380, 
abacus  o.  193.  If  the  members  thus  represented  accord  with 
our  conception  so  exactly,  we  have  a right  to  conclude  that 
the  same  would  be  found  true  of  those  concerning  which 
we  have  nothing  more  to  guide  us  than  the  following: 


Archi- 

trave. 

Frieze. 

Width 

of 

Column 

Width 

of 

Metope. 

Cornice. 

Abacus. 

Nemesis  at  Rhamnus 

0.575 

0.575 

0.558 

0.574 

0.212 

0.131 

Themis  at  Rhamnus  . . 

0.584 

0.586 

0.594 

0.582 

0.210 

0.154 

Minerva  at  Sunium  . 

0.834 

0.825 

0.793 

0.740 

0.39° 

0.196 

Neptune  at  Paestum  . 

i-492 

1.376 

1-434 

1.390 

0-797 

0.432 

Small  Temple  at  Paestum 

0.990 

O.9IO 

O.99O 

— 

— 

— 

Theseum 

0.835 

0.826 

0.778 

0.774 

0.346 

0.199 

At  Segesta  . ... 

1-447 

1.560 

1.326 

0.691 

0.375 

Diana  at  Eleusis  . 

0.642 

0.615 

0.628 

0.590 

0.363(7) 

0.181 

R.  at  Selinus  .... 

1. 729 

I. 721 

I-796 

r.380 

1.030 

0.508 

Concord  at  Agrigentum  . 

1. 106 

1. 106 

1.099 

0.932 

0.615 

0.316 

Juno  Lucina  at  Agrigentum 

1-053 

1-034 

1-073 

— 

— 

O.320 

Esculapius  at  Syracuse  . 

0-975 

0-975 

0.932 

— 

0.480 

— 

Minerva  at  Syracuse 

1.488 

1.407 

1.520 

— 

— 

0.445 

Parthenon 

1-347 

1.467 

1.304 

0.622 

0.346 

13 


194 


PROPORTION  AND  HARMONY. 


In  the  latter  building  we  have,  to  guide  us,  the  measure- 
ments of  Penrose  (sec.  2,  appendix,  page  1 14).  These  give 
us  the  metopes  all  the  way  from  4.050  at  the  extreme 
side  of  the  front  to  4.375  in  the  middle  of  it,  the  archi- 
trave 4.425,  and  the  frieze  4.417.  In  view  of  the  indi- 
cations of  paint  on  the  mouldings  above  the  latter  two 
in  the  temple  of  TEgina  which  gives  us  a right  to  surmise 
that  they  were  intended  to  have  the  effect  of  wide  divid- 
ing lines,  we  are  warranted  in  concluding  that  each  of 
these,  i.  <?.,  the  architrave  and  frieze  of  the  Parthenon, 
would  seem  about  twice  the  height  of  the  cornice,  which 
is  1.95 1,  and  which  differs  very  slightly  from  the  height 
of  the  stylobate,  namely,  1.814. 

There  are  other  temples  in  which  the  ratio  between  the 
cornice  and  architrave  seems  to  be  as  1 : 3.  Lloyd  says 
(C.,  appendix,  p.  75)  that  in  the  temple  of  Phigaleia,  “of 
the  entablature  proper,  three  sevenths  was  given  to  the 
architrave,  three  sevenths  to  the  frieze,  and  one  seventh 
to  the  cornice.”  Here  are  the  figures  (pi.  6):  architrave 
2' 7"  10,  frieze  2/7//50,  cornice  9^3 7,  and  the  upper  diameter 
of  the  columns — but  they  differ  in  size — 3/o'/8.  Notice 
too  that,  in  this  temple,  the  middle  step  of  the  stylobate 
measured  9,/883-  This  proportion,  1 : 3,  seems  to  be 
found  in  the  following  (H.): 


Archi- 

trave. 

Frieze. 

Width 

Upper 

Col. 

Width 

Metope. 

Cornice. 

Abacus. 

Ceres  at  Eleusis  .... 

1.696 

1.622 

1.620 

1-474 

0.567 

0.329 

Jupiter  at  Nemea  .... 

1.023 

1. 142 

I.060 

1. 137 

0.339 

0.260 

Apollo  at  Delos  .... 

Q-791 

0.770 

0.711 

0.660 

0.278 

0.203 

Jupiter  at  Olympia  . . . 

i. 670 

1.700 

I.696 

1.650 

0.680 

O.42O 

In  the  remaining  temples  the  proportions  seem  more 
like  2 : 3 or  3 : 4 : 


GREEK  ARCHITECTURAL  PROPORTIONS. 


195 


Archi- 

trave. 

Frieze. 

Width 

Upper 

Col. 

Width 

Metope. 

Cornice. 

Abacus. 

Corinth . 

1.440 

1-440 

I.323 

1.167 

1. 061 

0.327 

S.  at  Selinus 

1.516 

1.492 

1.248 

r. 250 

0.953 

0.334 

T.  “ “ 

2.332 

2.464 

1.940 

1. 618 

0.654 

D.  “ “ 

1.484 

1.482 

1. 149 

I.209 

r.029 

0.359 

C.  “ “ 

1.489 

I.502 

1. 123 

I.OO9 

0.386 

A.  “ “ 

1. 106 

1.054 

1.058 

O.902 

0.635 

0.275 

Giants  at  Agrigentum 

3-329 

3328 

2.983 

2.547 

1-374 

0.853 

When  we  take  into  consideration  the  mouldings,  which, 
if  included  or  excluded,  would  slightly  change  these 
figures  as  originally  recorded,  and  when  also  we  make  al- 
lowances for  the  mistakes  that  invariably  arise  in  copying 
and  re-copying  figures,  the  uniformity  of  these  results  is 
remarkable.  No  one  looking  at  them  can  doubt  that  the 
measurements  were  meant  to  produce  the  effect  of  putting 
like  with  like,  or  where  not  so  with  like  multiples  of  like. 

IV.  Once  more,  the  height  of  the  architrave  and  of  the 
frieze,  and  the  width  of  the  upper  diameter  of  the  columns, 
and  of  most  of  the  metopes,  bore  a relationship,  express- 
ible by  the  low  number  1 : 2,  to  the  combined  height  of 
the  architrave  and  frieze,  that  is,  of  the  entablature  with- 
out the  cornice,  and  also  to  the  height  of  the  tympanum,1 
except  where,  as  in  the  Parthenon,  this  was  equal  to  the 
height  of  the  whole  entablature,  and  also  to  the  apparent 
horizontal  distance  between  the  columns  just  under  their 
capitals.  As  will  be  pointed  out  on  page  263,  the  distance 
between  the  columns  at  the  extreme  sides  of  the  front 
was  less  than  between  the  others.  But,  as  will  also  be 
pointed  out,  this  less  distance,  in  all  cases,  was  intended 
to  appear  the  same  as  the  greater  distance.  The  apparent 
distance  between  the  columns  just  under  their  capitals 

1 By  the  tympanum  is  meant  that  part  of  the  pediment  which  was  between 
the  horizontal  and  the  raking  cornice. 


196  PROPORTION  AND  HARMONY. 

was  generally  the  same  as  the  height  of  the  entabla- 
ture without  the  cornice,  and  also  as  the  height  of  the 
tympanum.  There  was  undoubtedly  an  intended  propor- 
tion also  between  the  lower  diameter  of  the  columns  and 
the  lower  space  between  the  columns  and  the  height  of 
the  stylobate  or  foundation,  but  the  measurements  are 
not  sufficient  to  warrant  a positive  statement  of  what  this 
generally  was.  Lloyd  says  (C.,  appendix,  page  73)  that  in 
the  Propylaea  and  Parthenon  the  height  of  the  stylobate 
was  to  the  space  between  the  columns  as  2:1,  and  to 
the  diameter  of  the  column  as  3 : 2. 

In  confirmation  of  what  has  been  said,  it  will  be  noticed 
that  the  dimensions  of  every  architrave  and  frieze  given 
under  the  last  head  show  that,  as  each  was  intended  to 
appear  of  the  same  height,  both  together  would  be  to 
each  alone  as  2:1.  The  upper  distances  between  the 
columns  cannot  be  ascertained  in  a sufficient  number  of 
cases  to  furnish  demonstrative  proof ; but  all  the  carefully 
drawn  elevations,  like  those  of  the  west  front  of  the  Propy- 
laea and  of  the  Theseum  (Fig.  10,  page  36)  in  the  plates 
of  Penrose,  and  of  the  temples  at  yEgina  (Fig.  94,  page 
183)  and  Bassae  and  others  in  the  plates  of  Cockerill, 
show  that  the  effect  produced  is  that  of  twice  the  upper 
diameter  of  the  columns,  and  therefore  of  a measurement 
exactly  equalling  that  of  the  combined  architrave  and 
frieze.  That  the  latter  two  together  were  designed  in 
most  cases  to  have  the  same  apparent  height  as  the  tym- 
panum, is  evident  not  only  from  these  drawings,  which 
are  all  intended  to  represent  the  measurements,  but  also 
to  an  extent  from  the  measurements  themselves.  For  in- 
stance, in  C.,  pi.  4,  the  entablature  of  the  temple  at  ^Egina 
is  given  as  6'g"ygo,  and  the  pediment  as  7' 3".  But  if  we 
look  at  pi.  7,  we  find  the  architrave  2'gl'  and  frieze  2rg"2Z,, 


GREEK  ARCHITECTURAL  PROPORTIONS. 


I97 


together  5 '8"2  5 , and  if  from  j'l" , the  height  of  the  whole 
pediment,  we  take  the  height  of  the  raking  cornice  and 
cymatium  over  it,  the  measurements  of  which  are  not 
given,  but  are  apparently  fully  equal  to  that  of  the  hori- 
zontal cornice  with  mouldings  under  it,  which  is  repre- 
sented to  be  i'y"46$,  we  get  5'5*535,  which  would  very 
nearly  represent  the  height  of  the  tympanum.  The 
measurements  of  the  other  temples  will  be  found  on 
page  221. 

At  best,  however,  the  measurements  that  we  have  of 
the  pediment  and  tympanum  of  all  the  temples  examined 
are  exceedingly  unsatisfactory.  In  some  cases  it  could 
not  be  otherwise.  The  temples  are  in  ruins  and  the  ped- 
iments are  usually  the  first  to  disappear.  Even  where 
they  remain,  or  enough  of  them  to  indicate  what  their 
angles  were,  the  cymatium,  or  crowning  moulding  of  the 
raking  cornice,  is  usually  gone,  and  without  it  their  appar- 
ent heights  cannot  be  properly  estimated.  Some  temples, 
too,  had  what  was  called  the  acroterium,  an  ornament  on 
the  apex  which  increased  its  apparent  height.  (See  Fig.  94, 
page  183.)  But  in  addition  to  this,  those  who  have  made 
the  measurements  have  themselves  not  been  interested 
in  the  matter.  Penrose  has  nothing  in  connection  with 
any  bf  his  plates  to  indicate  the  measurements  of  the  tym- 
panum, raking  cornice,  or  cymatium,  although  in  his  text 
he  states  what  they  were.  In  the  case  of  the  Parthenon, 
Cockerill  ignores  them  altogether,  and  in  the  measure- 
ments collected  by  Hittorf  it  is  not  possible  to  make  out 
whether  the  tympanum  is  meant  or  the  whole  pediment, 
or  whether,  if  the  latter,  the  measurement  of  the  cymatium 
is  also  included.  This  is  the  more  unfortunate  inasmuch 
as  the  entire  question  concerning  the  Greek  idea  of  pro- 
portion depends  largely  on  the  relative  heights  of  these 


98 


PROPORTION  AND  HARMONY. 


members  of  the  front.  How  true  this  is,  and  what  mis- 
takes are  made  because  this  fact  is  not  recognized,  is 
evident  from  a book  that  lies  before  me  now,  “ The  Archi- 
tecture of  Marcus  Vitruvius  Pollio,”  translated  by  Joseph 
Gwilt.  Its  text  is  accompanied  by  plates.  In  six  of  these 
are  representations  of  temples  supposed  to  be  constructed 
in  the  Greek  style,  and  not  one  of  them  bears  much  more 
resemblance  to  the  Greek  style  than  a human  being  who 
could  be  a fit  subject  to  be  exhibited  in  a museum  on  ac- 
count of  his  deformity,  would  bear  to  a man,  and  this  largely 
because  of  the  disproportionate  size  of  the  pediment.  It 
is  possible  that  the  draftsman  of  these  pictures  supposed 
that  the  proportions  of  the  Parthenon  would  justify  his 
drawings,  but  he  has  altogether  missed  the  meaning  of 
that  which,  presumably,  he  desired  to  indicate.  However, 
notwithstanding  the  lack  of  data  and  interest  in  these  sub- 
jects, enough  measurements  have  been  made  to  sustain, 
though  only  in  a general  way,  the  principle  that  we  are 
trying  to  establish.  But  before  quoting  the  figures,  let 
us  state  another  fact  that  will  be  confirmed  by  them. 

V.  Not  only  was  the  apparent  height  of  the  entabla- 
ture under  the  cornice  or,  at  times,  under  only  the  corona 
of  the  cornice,  equal  to  that  of  the  tympanum,  but  the 
apparent  height  of  this  same  part  of  the  entablature,  in- 
cluding sometimes  the  abacus,  sometimes  it  and  also  the 
ovolo  under  it,  and  sometimes  the  whole  capital  of  the 
column,  was  equal  to  the  height  of  the  whole  pediment 
including  the  raking  cornice  and  cymatium  ; and  each  of 
these  heights  bore  to  the  height  of  the  column-space  be- 
neath it  a relationship  expressible  by  low  numbers,  like 
1:2,  1 : 3,  or  2:  3. 

The  variousness  of  result  thus  indicated  is  very  im- 
portant. It  solves  the  riddle  of  the  differences  that  we 


GREEK  ARCHITECTURAL  PROPORTIONS. 


I99 


find  in  the  measurements  and  proportional  measurements 
of  different  temples.  It  shows  us  how  the  Greek  artist 
could  manifest  originality,  and  yet  continue  to  carry  out 
the  first  principles  of  his  art.  The  differences  in  these 
measurements  are  found  not  only  in  the  heights  of  en- 
tablatures and  pediments,  but  also  still  more  of  columns. 
How  can  this  fact  be  reconciled  with  any  fixed  principle 
with  reference  to  proportion?  An  endeavor  to  answer 
this  question  will  be  made  in  Chapter  XII. 


CHAPTER  XII. 


THE  LARGER  DIVISIONS  OF  THE  FRONT  OF  THE  DORIC 

TEMPLE. 

The  Column-Space  and  the  Method  of  Principality — Proportion  on  the 
Flanks  of  Height  of  Columns  to  the  Entablature — Variety  of  Exact 
Proportions  on  the  Front  might  Arise  from  a Desire  to  Plave  Similar 
Apparent  Proportions — Difficulty  of  Determining  the  Line  of  Separa- 
tion between  the  Tympanum,  Entablature,  antf  Column-Spaces — Illus- 
trated in  the  Temple  at  yEgina — How  its  Tympanum  and  Entablature 
each  can  be  Made  to  be  to  Columns  as  i : 3 — How  Pediment  and  Entab- 
lature, Including  Capital,  each  can  be  Made  to  be  to  Shaft  as  1 :2 — How 
Rectangles  of  Front  in  Foundation,  Columns,  Entablature,  Pediment, 
etc.,  Are  all  in  Proportion- — Triangle  of  both  Tympanum  and  Pediment 
are  in  Proportion  to  Spaces  under  them — These  Arrangements  Illustrate 
the  Complexity  of  Harmony,  but  are  Analogous  to  those  of  Rhythm,  not 
Pitch — Illustrated  from  Temple  at  Basste — Entablature,  Pediment,  and 
Columns — Proportions  of  the  Rectangles  Formed  by  the  Front  Spaces — 
Temples  in  which  the  Abacus  is  Treated  as  Part  of  the  Entablature 
Space — Proportions  of  the  Rectangles  of  the  Front  in  Propylsea  and 
the  Theseum — The  Parthenon  at  the  Beginning  of  a Transition — De- 
parture in  it  from  Former  Methods — How  these,  nevertheless,  Conform 
to  the  Principles  here  Unfolded — Other  Subordinate  and  Complementary 
Proportions — All  Tending  to  Produce  General  Harmony  of  Effect. 

/E  have  reached  a place  where  we  must  consider  the 
proportions,  each  to  each,  of  the  heights  of  the 
pediment,  the  entablature,  and  the  columns,  which  to- 
gether, with  the  less  important  stylobate,  or  foundation, 
made  up  the  whole  front  of  the  Greek  temple.  Of  these, 
the  principal,  or  distinguishing,  feature  was  undoubtedly 
the  row  of  columns  through  which  the  worshipper  entered. 
The  law  of  principality,  therefore,  as  unfolded  in  Chapter 


200 


PROPORTIONS  OF  GREEK  TEMPLES — FRONT.  201 


V.  of  “ The  Genesis  of  Art-Form,”  would  require  the  em- 
phasizing of  the  vertical  space  given  to  these  columns. 
We  find  that  it  was  emphasized.  In  all  cases  it  was  made 
larger  than  that  given  to  any  other  feature  ; and  in  most 
cases  larger  than  that  given  to  all  the  other  features  com- 
bined. “ It  appears,”  says  Lloyd  (P.,  appendix,  page  1 12), 
“that  the  greatest  importance  was  attached  to  making  the 
height  of  the  column  exceed  the  joint  height  of  the  other 
members,  that  is,  stylobate,  entablature,  and  pediment, 
by  a single  aliquot,  ...  in  other  words,  the  height 
of  the  column  may  compare  with  the  complementary 
height  of  the  front  as  7 : 6 or  6 : 5.”  The  ratio  applied  in 
the  Parthenon,  he  tells  us,  is  10  : 9 ; at  Bassae,  7:6;  in  the 
Theseum,  5 : 4.  On  the  sides  both  of  the  Parthenon  and 
Theseum,  where,  of  course,  there  is  no  pediment,  the  ratio 
of  the  height  of  the  column  to  that  of  the  joint  founda- 
tion and  entablature,  which  latter  is  made  higher  by  the 
ornament  above  the  cornice  called  the  cymatium,  is  2 : 1, 
and  at  Bassae  there  is  a close  approximation  to  this  (C., 
appendix,  page  72).  The  exact  measurements  are  usually 
given  by  Lloyd,  but  there  is  no  need  of  quoting  them 
here. 

They  become  important  only  as  we  advance  a step  far- 
ther. It  has  been  said  that  the  features  attracting  atten- 
tion in  the  Greek  temple  are  the  columns,  the  entablature, 
the  pediment  inclosing  the  tympanum,  and  the  founda- 
tion. The  proportions  of  the  columns,  entablature,  and 
foundation,  as  determined  without  reference  to  the  tym- 
panum, may  be  studied  on  the  flanks,  or  sides,  of  the 
buildings,  as  well  as  on  their  fronts.  Examining  them 
on  the  flanks,  we  find  that  in  the  temple  of  Phigaleia  (C., 
pi.  3)  the  columns  (19'  5"  125)  are  to  the  height  of  the 
entablature  (6'  5"  208)  as  3 : 1.  In  the  Parthenon  (Fig. 


202 


PROPORTION  AND  HARMONY, , 


9 6,  page  190)  the  entablature  is  10.794,  which,  added  to 
the  fillet  of  the  cymatium  above  it,  0.299,  gives  us 
11.093,  and  this,  as  we  are  told,  is  to  34.288,  the  height 
of  the  column,  very  nearly  as  1 : 3 (P.,  appendix,  page  14). 
One  would  naturally  infer  that  if  such  simple  propor- 
tions were  used  on  the  flanks,  they  would  be  used  on  the 
fronts ; and  it  will  be  shown  presently  that  this  inference 
is  justified.  But  although  1 : 3 is  the  very  ratio  employed 
by  Lloyd  when  speaking  of  the  flank  effects  of  the  Par- 
thenon, he  says  (P.,  ap.  page  1 12),  “ the  ratios  1 : 3 and  2 : 5 
are  most  extensively  and  importantly  employed  in  the 
temple  at  Bassae,  but — referring  evidently  only  to  the 
front  effects — are  absolutely  unknown  in  the  Parthenon.” 
Other  reasons  for  doubting  this  statement,  besides  the 
one  thus  indicated,  will  be  given  hereafter. 

Taken  just  as  they  are  reported,  many  of  the  measure- 
ments of  the  fronts  of  temples  do  not  indicate  with 
exactness  any  proportional  ratios.  From  what  was  said, 
however,  on  page  165,  of  an  excusable  absence  of  ap- 
parent ratios  between  sets  of  measurements,  as  well  as 
on  page  35  of  judging  architectural  effects  from  a distance, 
one  might  take  the  ground  that  the  measurements  need 
not  indicate  proportions  exactly,  because  approximate 
proportions  are  all  that  can  be  recognized  from  a distance. 
One  might  say,  therefore,  that  these  are  all  that  are  neces- 
sary. But  he  may  do  more  than  this.  He  may  say  that, 
owing  to  certain  peculiarities  of  situation  or  of  shape, 
these  are  all  that  are  not  misleading.  Very  often  it  is 
impossible  for  one  form  to  be  made  to  appear  just  the 
size  of  another,  unless  its  real  size  is  lessened  or  increased. 
Stripes,  for  instance,  as  said  once  before,  tend  to  lengthen 
the  effects  of  fabrics  in  the  direction  in  which  they  run. 
A space  filled  with  upright  columns,  therefore,  naturally 


PR OP OR  7 VO  NS  OF  GREEK  TEMPLES — FRONT.  203 


seems  higher  in  proportion  than  one  filled  by  an  entab- 
lature, in  which  most  of  the  lines  are  horizontal.  This 
fact  alone  would  justify  the  architect  of  the  Parthenon 
and  of  the  temples  at  Corinth  and  Nemea  in  making  the 
columns  a little  shorter  than  would  be  necessary  in  order 
to  make  the  actual  ratios  exactly  2 : 1,  3 : 1,  or  4 : 1. 

Now,  however,  we  come  to  a still  more  important  con- 
sideration. It  is  not  at  all  certain  that  the  line  which  we 
suppose  to  separate  one  feature,  like  a cornice  or  archi- 
trave, from  another  made  proportional  to  it,  is  the  line  by 
which  the  Greek  builder  intended  to  indicate  the  bound- 
ary between  the  two.  For  instance,  did  the  measurement 
for  the  rectangle  of  which  the  entablature  is  the  chief 
feature,  always  begin  above  the  capital  of  the  column  and 
end  above  the  cornice?  Undoubtedly  it  did  sometimes, 
especially  upon  the  flanks,  where  there  was  no  necessity 
for  any  feature  below  the  entablature  proper  to  balance 
the  raking  cornice  and  cymatium  that  were  above  the  pedi- 
ment. But  if  anyone  will  glance  along  a colonnade,  he 
will  perceive  that  the  bottom  of  the  abacus — i.  e.,  the  flat 
stone  parallel  to  the  entablature,  forming  the  top  member 
of  the  column’s  capital  (see  Fig.  93,  page  182) — forms  just 
as  effective  a dividing  line  for  the  eye  as  the  bottom  of 
the  entablature  proper.1  The  same  might  be  affirmed, 
especially  in  connection  with  the  Ionic  and  Corinthian 
orders  (Figs.  9 7,  page  204  ; 98,  page  220),  of  the  whole  capi- 
tal.1 The  fillet,  moreover,  which  is  at  the  top  of  the  entab- 
lature’s horizontal  cornice  and  is  carried  all  around  the 
pediment,  as  well,  too,  as  around  the  whole  corona  of  the 
cornice  (Fig.  93,  page  182),  may  form  an  equally  effective 
dividing  line  between  the  entablature  and  the  pediment. 

1 Since  writing  this,  the  author  has  found  a similar  suggestion  in  Figs.  I, 
2 and  3 of  the  “ Theorie  des  Proportions”  of  P.  Faure. 


204 


PROPORTION  AND  HARMONY. 


1 III  11“ 

'in111"  111 

III  HI11  '«»«  nl|||!lll||jH 

mm\ 

l!|i||ii  ill 

11 

|ll!r  '111  1 1 

There  is  no  fagade  more  suggestive  of  exact  propor- 
tions than  that  of  the 
temple  of  ^Egina  (Fig. 


■jzjz  _ L. r 1 


94,  page  183),  yet  the  ap- 
parent ratios  on  page 

196  are  as  much  astray 
when  applied  to  it  as  to 
any  other  of  the  temples. 
Moreover,  the  ratios  seem 
still  more  astray  when  we 
examine  them  more  care- 
fully (C.,  plate  4).  We 
discover  that  the  columns 
measure  1 7'  2"  8,  the  en- 
tablature 6'  9"  790,  and 
the  pediment  7'  3"  o. 
There  are  no  indisput- 
able ratios  to  be  made 
out  of  these  numbers, 
and  yet,  as  was  said,  the 
proportions  of  the  build- 
ing, as  one  looks  at  it, 
seem  unusually  satisfac- 
tory. If  the  fault  be  not 
in  the  building,  it  must 
be  in  the  way  in  which 
it  has  hitherto  been  sup- 
posed that  the  ratios  were 
determined. 

We  ascertained  on  page 

197  that  the  tympanum 
of  this  temple  measured 

this  tympanum  came  the  cor- 


nu. 97. 

IONIC  COLUMN  AND  ENTABLATURE. 

See  pages  203,  219,  220. 


about  5 ' 7"  6.  Under 


PROPORTIONS  OF  GREEK  TEMPLES — FRONT.  205 

nice,  the  distinguishing  feature  of  which  was  the  flat 
corona,  and  this  measured  7,/  675.  Under  the  corona 
came  the  architrave  and  frieze,  the  two  together  meas- 
uring 5' 6"  25,  or,  if  we  include  a slight  moulding  under 
the  corona,  5'  7 875-  Under  these  came  the  abacus 
measuring  7'' 6 50,  the  same  as  the  corona.  Under  the 
abacus  came  the  rest  of  the  column,  measuring  in  all 
17'  2"  8,  or  16' 5" 150  without  the  abacus.  One  third  of 
this  latter  number  is  5'  5"  05.  Recalling  now  that 
straight  lines  increase  the  apparent  length  in  the  direction 
in  which  they  point,  we  see  that  here  are  three  heights 
which  are  in  proportion,  viz.  : tympanum  to  entablature- 
height  without  the  corona  of  the  cornice,  as  1 : 1 ; each  of 
these  to  the  height  of  the  columns,  as  1 : 3 ; and  both  to- 
gether to  the  height  of  the  columns,  as  2 : 3. 

But  this  is  not  all.  These  three  heights  do  not  touch 
one  another,  but  are  separated  by  members  having  the 
effects  of  broad  dividing  lines.  Some  one  may  ask, 
Should  not  the  proportions  include  the  entire  space  ex- 
clusive of  dividing  lines  ? We  will  let  them  do  this. 
Take  the  height  of  the  pediment,  ’]'  3"  o,  and  add  to  it 
that  of  the  entablature,  6'  9"  790,  and  of  the  capital  of 
the  column  including  abacus  7^650,  and  ovolo  i'c/75: 
result  l6T'igo.  Now  take  the  capital  from  the  column 
and  we  have  left  15' 4"  400,  enough  shorter  to  make  its 
upright  lines  seem  to  the  horizontal  above  (page  202) 
as  1:1.  Half  of  16VT90  is  8'o"595.  We  have  found 
that  the  pediment  measures  f . C.,  pi.  7,  shows  us  that 

above  the  corona  of  the  horizontal  cornice  there  are  sev- 
eral small  mouldings  measuring  2;,8,  2/,o,  and  TT25  ; all 
together,  5"925.  Adding  this  to  f 3"  we  get  7'&"g2$, 
within  about  two  feet  of  the  middle  point  of  the  space 
above  the  columns.  If  we  look  at  the  front  again,  especially 


206 


PROPORTION  AND  HARMONY. 


where,  as  in  some  large  illustrations,  it  is  colored,  we  shall 
see  that  the  effects  of  these  mouldings  above  the  horizontal 
cornice  clearly  belong  to  the  pediment.  The  pediment, 
therefore,  is  to  the  height  of  the  entablature-space  as  thus 
indicated  as  I : I,  and  each  to  the  column-height  as  i : 2. 

Now  if  we  look  again  we  notice  that  the  stylobate  or 
basement  of  this  temple  measures  3'8/,25.  This  is  only  a 
few  inches  less  than  one  half  of  7' 7" 200,  or  than  one 
quarter  of  the  height  of  the  column.  According  to  prin- 
ciples sometimes  exemplified,  this  is  what  we  should  ex- 
pect. The  near  and  low  members  are  made  slightly  smaller, 
so  as  to  seem  of  the  same  size  as  the  remote  and  elevated 
members.  In  this  temple,  the  stylobate  represents  I (3' 
8*25),  the  columns  below  the  ovolo,  4 and  the 

entablature-space  and  pediment  each  a little  in  excess  of 
2 (S'c/598),  and  both  the  latter  together,  a little  in  excess 
of  4 (16VT90).  Once  more,  the  breadth  of  this  temple 
is  given  as45T"9.  This  would  make  the  proportions  of 
the  rectangle  formed  by  the  general  outlines  of  the 
height  and  width  of  the  stylobate  about  1 : 12  ; of  the  por- 
tico below  the  capitals,  4 : 12  ; of  the  capitals  with  the  en- 
tablature, and  of  the  pediment,  each  2 : 12  ; of  the  stylobate, 
portico,  capitals,  and  entablature,  all  together,  7 : 12  ; of  the 
same  without  the  stylobate,  6:12;  and  of  the  whole  height 
to  the  breadth  9 : 12,  or  3 : 4.  Besides  this,  inasmuch  as 
the  larger  members  measure,  as  a rule,  just  twice  as  much  as 
the  smaller  members,  it  follows  that  these  larger  members 
are  all  in  proportion  to  the  smaller  members.  It  has 
been  shown  already  that  while  pediment  entablature  and 
capitals  are  to  portico  below  as  1:2,  tympanum  and 
entablature  without  the  cornice  are  to  the  same  as  1 : 3. 
It  could  be  shown  also  that  the  whole  cornice,  I '7 "46 5, 
and  probably  the  raking  cornice  and  cymatium,  the  meas- 


PROPORTIONS  OF  CREEK  TEMPLES — FRONT.  207 


urements  of  which  are  not  given,  are  intended  to  have 
the  same  effect  of  height  as  the  capital  of  the  column, 
At  any  rate,  the  raking  cornice  and  cymatium 
are  perfectly  balanced  by  the  effect  of  the  capitals  of  the 
columns  in  case  we  consider  them  to  be  treated  like 
pendants  of  the  entablature. 

If  at  the  top  of  the  corona  of  the  horizontal  cornice 
where  are  situated  the  mouldings  that  have  been  men- 
tioned, we  could  fold  the  angle  of  the  pediment  down- 
ward, its  apex  would  be  just  on  a line  with  the  bases  of 
the  capitals.  In  fact,  it  is  well  to  notice  that  above  the 
rectangular  entablature  space  we  have  two  triangles,  the 
smaller  one  of  the  tympanum,  the  lines  of  which  are 
inside  of  the  raking  cornice  (see  Fig.  94,  page  183),  and 
the  larger  one  of  the  pediment,  which  includes  the  former, 
and  the  lines  of  which  are  outside  of  the  cymatium. 
Each  of  these  appears  to  be  of  exactly  the  height  of  a 
rectangle  under  it.  The  first  is  of  the  height  of  the 
smaller  rectangle  formed  by  the  architrave  and  frieze  of  the 
entablature  ; the  second  is  of  the  height  of  the  larger  rec- 
tangle outlined  above  by  the  horizontal  cornice,  and  below 
by  the  bases  of  the  columns’  capitals.  Both  the  tympanum 
and  whole  pediment  therefore  appear  to  be  exactly  con- 
formed to  a rectangle  under  them.  This  arrangement,  as 
will  be  noticed,  corresponds  to  that  complexity  of  effect 
already  pointed  out  on  page  156  in  the  cathedral  at  Co- 
logne; on  page  170,  in  the  Grand  Opera  House  at  Paris; 
and  on  page  175,  in  the  Arch  of  Septimius  Severus.  In- 
deed, all  through  the  front  of  this  Greek  temple,  as  of 
these  other  buildings,  there  are  these  correspondences, 
which,  on  account  of  their  blendings  of  almost  countless 
effects,  may  be  said,  in  a general  way,  to  manifest  the 
harmony  of  proportion.  At  the  same  time  it  needs  to  be 


208 


PROPORTION  AND  HARMONY. 


emphasized  again  that  this  harmony  results  from  putting 
like  effects  together  according  to  the  principles  under- 
lying not  pitch  but  rhythm. 

The  proportions  of  the  temple  of  .TEgina  have  been 
used  to  illustrate  these  facts,  simply  because  they  are  ac- 
cessible, and,  as  will  be  shown  presently,  when  we  quote 
the  more  general  measurements  of  Hittorf’s  summary,  be- 
cause they  represent  a type.  Another  temple  of  which 
we  have  measurements  sufficient  for  our  purpose  is  that 
of  Phigaleia  (the  same  as  Bassse).  One  who  had  not  had 
experience  of  the  intricacies  of  Greek  proportion  would 
be  greatly  pleased  with  his  first  examinations  of  this  tem- 
ple (C.,  pi.  3):  columns  1 g'  5 " 125,  entablature  6'  5"  208. 
It  seems  evident  at  once  that  this  means  3 : 1.  There  is 
another  way,  however,  of  interpreting  the  meaning  of  these 
measurements.  The  pediment-height  is  not  given  ; but 
adding  together  the  stylobate,  2' 5"  833,  and  the  column 
and  entablature  as  already  given,  we  get  28' 6"  166;  and 
as  the  whole  height  is  given  as  36' o"  166,  we  infer  that 
the  pediment-height  is  y' 4".  Taking  a hint  from  what 
we  have  learned  from  the  temple  of  Aigina,  let  us  take 
from  the  entablature  (C.,  pi.  6)  the  mouldings  above  the 
corona  of  the  horizontal  cornice  (2"  75),  and  add  them  to 
the  pediment.  The  result  is  y'  6"  y 5-)-.  Let  us  next, 
after  taking  this  2*75  from  the  entablature,  add  to  it 
the  abacus,  y" \ 25,  and  the  ovolo,  7//87 5,  and  the  rest 
of  the  capital  of  the  column,  4ff75C>.  The  result  is  W2" 
208.  Let  us  now  take  the  combined  height  of  the 
abacus,  ovolo,  and  the  rest  of  the  capital  from  the  full 
height  of  the  column.  The  result  is  iy'$"?)y$'  Now 
look  at  the  stylobate  (C.,  pi.  3).  It  is  2/5"833.  Take  a 
very  few  inches  from  this  and  it  will  equal  one  seventh 
of  I7V375  ; and  take  a still  smaller  amount,  and 


FRONTS  OF  GREEK  TEMPLES. 


209 


it  will  equal  one  third  of  ’]'€>"’] 5.  Following  the  princi- 
ple suggested  in  the  case  of  the  temple  of  Afgina,  in  ac- 
cordance with  which  (page  202)  the  upright  members  are 
made  slightly  shorter  than  the  horizontal  ones,  we  have 
this  result : height  of  foundation  to  that  of  the  column-space 
excluding  the  capital  is  1:7;  height  of  the  entablature- 
space  including  the  column’s  capital,  and  also  height  of 
the  pediment-space  to  the  height  of  the  column-space, 
each  as  3 : 7 ; together  as  6:7;  the  combined  height  of 
stylobate  and  column  as  far  up  as  to  the  base  of  the 
capital  to  the  whole  height  above  this  is  as  8 : 6,  or  4 : 3. 
Or,  if  we  take  the  combined  height  of  the  stylobate  and 
of  the  whole  column  (22V'958,  or  if  only  to  the  abacus, 
2i/3"833)  we  get,  as  a result,  to  the  combined  height 
above  it  (in  the  one  case,  i3'9"2o8;  in  the  other  i4/6//333), 
the  ratio  very  nearly  of  3:2. 

The  breadth  of  this  temple  is  given  as  48'  2"  66.  If 
we  take  the  height  of  the  stylobate  for  our  standard,  this 
will  make  the  proportion  of  the  rectangle  of  the  stylobate 
— by  which  is  meant  the  ratio  of  the  height  to  the  breadth — 
1 : 1 8 ; of  the  column-space  to  capital,  7 : 18;  of  entablature- 
space  above  this  and  pediment  3 : 18,  or  1 : 6,  or  together 
6 : 18,  or  1 : 3 ; and  of  the  whole  front  14  : 18,  or  7 : 9.  The 
actual  proportions,  however,  are  more  like  3 : 4,  which 
could  be  obtained  by  averaging  the  heights  of  the  mem- 
bers. In  the  drawings,  the  tympanum  of  this  temple  seems 
intended  to  appear  of  the  same  height  as  the  entablature 
below  the  corona  of  the  horizontal  cornice.  Assuming 
this  to  be  the  case,  adding  together  (C.,  pi.  6)  architrave, 
2'  8"  75,  frieze,  2' 9"  083,  and  moulding  under  corona,  1"  660, 
we  get  5/9"493.  This  is  to  the  column  below  the  7^125 
of  the  abacus,  i.  e.,  to  l8'8",  about  as  3 : 10. 

In  the  two  temples  that  have  been  considered,  the 


210 


PROPORTION  AND  HARMONY. 


whole  height  from  the  base  of  the  column  to  the  apex  of 
the  pediment  seems  to  have  been  divided  into  equal  parts 
at  the  bottom  of  the  column’s  capital.  The  same,  as  we 
shall  find  presently,  was  true  of  the  Parthenon.  In  other 
temples,  this  division  seems  to  have  been  made  at  the 
bottom  of  the  abacus  of  the  capital.  One  of  these  is  the 
Propylaea  at  Athens,  the  central  temple  in  Fig.  95,  page 
186  (P.,  pi.  30).  Here  the  pediment  measures  9.747,  the 
entablature  8.849,  ar>d  the  column  28.134.  If  we  take  the 
height  of  the  abacus  (P.,  pi.  31),  .96,  from  the  column,  we 
have  left  27.174.  If  we  add  this  .96  to  the  entablature,  we 
get  9.80,  almost  exactly  the  height  of  the  pediment,  and 
only  a small  fraction  larger  than  one  third  of  the  height 
of  the  column,  the  proportions  of  which  to  the  entablature 
and  pediment  therefore  would  appear  to  be  3 : 1.  In  this 
temple  too,  as  in  yEgina  and  Bassae,  the  tympanum  and 
the  entablature  below  the  corona  of  the  cornice  seem  to 
be  of  exactly  the  same  height.  In  the  Theseum,  too  (Fig. 
10,  page  36),  all  these  proportions  seem  to  be  determined 
as  in  the  Propylaea,  but  (P.,  pi.  35)  they  are  not  indicated 
in  sufficient  detail  to  prove  this. 

Nor  in  either  of  these  two  temples  are  the  measure- 
ments sufficient  to  indicate  unmistakably  the  proportions 
of  the  rectangles  formed  by  the  spaces  devoted  to  the 
columns,  entablatures,  and  pediments.  But  if  the  breadth 
of  the  west  front  of  the  Propylaea  be  taken  at  about  72, 
as  seems  to  be  indicated,  its  entablature,  as  calculated 
with  the  abacus  (see  page  203),  being  a little  over  9,  and  its 
columns  27.174,  we  have  for  the  rectangle  of  entab- 
lature 1 : 8,  of  the  columns,  3 : 8,  and  of  both  together, 
4 : 8,  or  1:2;  and  of  the  whole  with  the  pediment  5 : 8. 
This  figure  8 corresponds,  as  will  be  noticed,  with  the 
regularity  of  the  effect  produced  in  this  temple  by  sepa- 


FRONTS  OF  GREEK  TEMPLES. 


21 1 


rating  the  columns  of  the  front  into  two  parts,  three 
columns  being  on  each  side  with  a very  wide  intercolumn- 
space  in  the  middle.  See  the  middle  temple  in  Fig.  95, 
page  186. 

Of  the  Theseum  (Fig.  10,  page  36),  the  breadth  is  given 
as  45.011,  the  height  of  the  front  entablature  with  abacus 
as  suggested  on  page  203,  6.2,  and  of  the  columns  18-}-  ; 
and  the  proportions  of  height  to  breadth  are  perhaps 
meant  to  appear  in  the  entablature  like  1 : 7,  in  the  column- 
space  like  3 : 7,  and,  in  both  together  like  4 : 7,  or,  including 
the  pediment,  like  5 : 7. 

It  is  ordinarily  supposed  that  the  Parthenon  represents 
the  highest  point  of  perfection  reached  by  Greek  archi- 
tecture. It  does,  and  yet  it  was  the  beginning  of  a de- 
cline, just  as  we  recognize  to  have  been  the  case  with  the 
poetry  of  Milton  and  the  music  of  Wagner,  when  we  no- 
tice the  effects  that  the  works  of  each  produced  upon  their 
followers  and  imitators.  The  Parthenon  is  the  building 
which  modern  people  have  studied  and  imitated  most  in 
their  efforts  to  understand  and  apply  the  Greek  methods. 
They  ought  to  have  it  impressed  upon  their  minds  that 
those  who  first  began  to  study  and  imitate  it  were  the 
ones  who  began  that  very  process  of  degeneracy  in  art, 
the  current  of  which  it  is  now  supposed  by  some  that  a 
return  to  Greek  methods  can  stem. 

The  architect  of  the  Parthenon  (Fig.  96,  page  190)  had 
not  ceased  to  be  controlled  by  the  principles  which  had 
been  exemplified  in  the  earlier  Doric  structures  ; but  he 
suggested  that  such  was  the  case,  and  others  soon  carried 
out  his  suggestions  to  their  logical  results.  According  to 
Lloyd  (P.,  appendix,  page  1 14),  the  height  of  the  column 
in  this  building  was  34.253,  of  the  front  entablature,  10.- 
794,  and  of  the  pediment,  14.073.  Here  is  great  appar- 


212 


PROPORTION  AND  HARMONY. 


ent  irregularity.  How  in  this  case  is  like  put  with  like? 
Can  any  simple  ratio  such  as  can  be  easily  recognized 
apply  to  these  figures?  It  can.  The  building  is  one  of 
those  examples  which  we  often  find  in  the  highest  art, 
in  which  exact  regularity  is  produced  through  apparent 
irregularity. 

In  this  case  again,  as  in  most  of  the  others  that  have 
been  mentioned,  take  the  capital  of  the  column  which 
measures  2.833  and  add  it  to  the  entablature.  The  result 
is  13.627,  which  from  below  to  one  looking  upwards,  es- 
pecially when  comparing  a rectangle  with  a triangle 
pointed  at  its  centre,  would  appear  to  be  to  the  14.073  of 
the  pediment  above  as  1 : 1.  This  capital  of  the  column, 
moreover,  exactly  balances  the  pediment’s  combined  rak- 
ing cornice  (1.174),  and  cymatium  (1.430),  i.  e.  (2.604), 
which  two  as  seen  from  below,  owing  to  the  projections 
of  the  cornice,  would  appear  slightly  higher  than  this. 
Here,  too,  as  in  the  temple  of  Higina,  if  at  the  edge  of 
the  horizontal  cornice,  the  pediment  were  folded  down 
over  the  entablature,  its  apex  would  be  on  a line  with  the 
bottoms  of  the  columns’  capitals.  Taking  the  height  of 
the  capital  now  from  the  column,  we  have  left  31.420, 
and  adding  the  capital  to  pediment  and  entablature- 
space  above  this,  we  have  27.700.  It  is  conceivable,  con- 
sidering the  height  of  the  pediment,  that  these  numbers 
were  intended  to  produce  the  effect  of  a ratio  of  7:6. 
27.254,  twice  the  combined  capital  and  entablature  height 
with  which  the  column-space  below  is  immediately 
compared,  would  represent  this  ratio  still  more  nearly. 
The  height  of  the  foundation  is  6.050,  just  enough  less 
than  half  of  13.627,  the  height  of  the  entablature-space, 
to  accord  with  the  principle  which  we  have  found  every- 
where exemplified,  that  the  near  and  low  member  is  made 


FRONTS  OF  GREEK  TEMPLES. 


213 


slightly  shorter  than  the  remote  and  high  one.  The 
heights  of  the  different  members  of  the  front  may  there- 
fore be  proportioned  thus  : that  of  the  stylobate  to  that 
of  the  column-space  excluding  capital  of  column,  3:14; 
that  of  the  capital  of  column  with  entablature,  as  also 
that  of  the  pediment,  to  that  of  the  column  aside  from 
capital,  3:7;  and  both  the  former  together  to  both  the 
latter  as  6:7.  These  figures  suggest  what  Lloyd  (P., 
appendix,  page  112)  says  with  reference  to  the  prevalence 
of  certain  ratios  similar  to  these  in  the  Parthenon, — 
for  instance  ; that  its  height  is  to  its  length  as  2:7,  its 
height  to  its  breadth  as  9 : 14,  and  its  length  to  its 
breadth  as  4 : 9.  See  page  217. 

The  proportions  that  have  been  indicated  in  the  front 
height  of  this  building,  however,  are  not  all  that  it  is  impor- 
tant to  notice.  As  in  the  case  of  the  other  temples  that 
we  have  considered,  it  contained  other  subordinate  or 
complementary  proportions,  intended  to  be  blended  with 
these,  and  thus  to  secure  that  complexity  of  effect  already 
noticed  as  applied  to  other  buildings  (see  pages  170  and 
175),  and  which,  as  shown  in  Chapter  XIII.  of  “Art  in 
Theory,”  is  an  important  constituent  of  harmony. 

If  instead  of  taking  the  whole  capital  from  the  column 
and  adding  it  to  the  entablature,  we  take  only  the  abacus 
1. 155,  we  have  left  for  the  column  33.098,  for  the  entabla- 
ture, 10.794  -(-  1. 155,  i.  e.,  H-949  (P-,  sec.  2).  But  the 
pediment,  14.073,  without  the  raking  cornice,  1 . 1 74,  and 
the  cymatium,  1.430 — in  other  words,  the  tympanum  of 
the  pediment  measures  11.469.  Thus  calculated,  the 
height  of  the  front,  excluding  the  corona  of  the  pediment, 
gives  us  for  the  columns  3,  for  the  entablature  1,  for  the 
tympanum  1.  Even  the  stylobate,  6.050  is  not  so  far 
from  one  half  of  1 1.949,  that  it  would  not  seem  to  blend 


214 


PROPORTION  AND  HARMONY. 


harmoniously  witli  the  proportions  thus  suggested,  giving 
us  in  all  for  the  height  of  the  stylobate  i,  of  columns  6, 
of  entablature  with  abacus  2,  and  of  tympanum  2.  This 
would  leave  out  of  the  calculation  the  raking  cornice  and 
cymatium  of  the  pediment.  But  we  have  already  shown 
another  method  of  division  in  which  they  would  be  in- 
cluded. Let  us  now  notice  still  another  method  (P.,  ap- 
pendix, page  1 14).  The  height  of  the  pediment  was 
14.073,  of  the  entablature  10.794,  of  the  abacus  1.155, 
making  together  26.022,  or  without  the  cymatium  (1.430), 
24.592.  If  we  divide  the  former  of  these  last  numbers  by 
three  we  get  8.674;  if  the  latter,  we  get  8.197.  But  the 
height  of  the  column,  34.253,  excluding  the  abacus,  is  33  - 
098.  Dividing  this  by  4 we  get  8.274.  Taking  into  con- 
sideration what  has  been  said  before,  that  the  upright 
lines  of  the  columns  always  have  the  effect  of  increasing 
their  apparent  height,  we  can  say  that  the  proportion  be- 
tween the  height  of  the  column-space  here  and  of  the 
space  above  it,  was  meant  to  appear  to  be  as  4 : 3.  In- 
deed, if  we  exclude  the  cymatium,  it  was  almost  exactly 
this.  Moreover,  this  space  above  the  columns  seems  to 
have  been  divided  into  three  parts  by  way  of  suggestion, 
the  lower  part  being  separated  from  the  next  higher 
by  the  chief  continuity  of  line  suggested  by  the  figures  in 
the  metopes  of  the  frieze,  and  the  next  from  the  very 
highest  by  that  of  the  figures  in  the  tympanum.  At  any 
rate,  whether  we  concede  the  existence  of  these  suggested 
divisions  or  not,  there  is  no  doubt  about  the  main  fact 
that  the  columns’  height  to  the  height  above  them  would 
appear  as  4 : 3. 


CHAPTER  XIII, 


OTHER  GREEK  ARCHITECTURAL  MEASUREMENTS  AND 
GENERAL  CONCLUSIONS. 

Unusual  Size  of  the  Tympanum  of  the  Parthenon — Reasons  for  this — Pro- 
portions of  the  Rectangles  of  the  Front  of  the  Parthenon — Same  Prin- 
ciples Revealed  in  the  Measurements  of  Other  Temples — Exact  Squares 
Formed  by  the  Width  and  Height  of  Three  Adjacent  Columns  in  Many 
Temples — Proportion  between  the  Diameters  and  Heights  of  Many 
Columns — Measurements  from  Twenty-three  Doric  Temples  Verifying 
the  hitherto  Unverified  Statements  in  Chapters  X.  and  XI. — Why  the 
Doric  Temples  are  Chosen  for  Illustrations — After  Experiment  had 
Determined  the  Laws  of  Proportion,  Art  Imitated  and  Degenerated — 
Because  Artists  no  longer  Followed  out  the  Natural  and  Instinctive  Art 
Tendency,  Founded  upon  Comparison — This  Tendency  Apparent  in 
that  which  Originated  the  Gothic  and  Renaissance  Styles — No  Great 
Architecture  without  it — Possibilities  of  Architecture  not  Exhausted 
but  must  be  Developed  from  the  Principle  of  Comparison. 

r|’  HE  details  of  measurement  in  the  case  of  the  Parthe- 
non have  been  explained  so  fully,  in  order  to  reveal 
how  careful  the  Greek  architects  were  to  carry  out  the 
general  principle  underlying  their  methods  of  construc- 
tion even  when  they  differed  in  the  applications  of  it  to 
details.  The  difference  between  the  Parthenon  and  the 
other  temples  that  have  been  examined  was  in  the  size  of 
the  tympanum.  In  those,  the  height  of  this  was  equal  to 
that  of  the  entablature  under  the  corona  of  the  horizontal 
cornice  ; in  the  Parthenon,  to  that  of  the  whole  entabla- 
ture together  with  the  abacus.  The  important  matter  for 
us  to  observe  is  that,  nevertheless,  the  tympanum  and  the 

215 


2l6 


PROPORTION  AND  HARMONY. 


pediment,  also,  were  made  just  equal  to  the  height  of 
something,  and  in  exact  proportion  to  something  else. 
More  than  this,  too,  there  were  so  many  parts  of  these 
members  that  could  be  compared  to  other  parts,  and  so 
many  different  ways  of  making  out  the  proportions  in- 
tended, that,  no  matter  what  the  observer’s  theory  might 
be,  he  could  have  no  doubt  that  in  some  way  the  general 
laws  of  proportion  were  fulfilled.  This  was  the  complexity 
of  result  at  which  the  Greek  architect  seems  to  have 
chiefly  aimed.  And,  in  view  of  this  fact,  the  Parthenon 
is  particularly  interesting,  because,  involving  as  it  did  a 
departure  from  ordinary  methods,  it  would  evidently  be 
essential  that  in  it  this  complexity  should  be  especially 
suggested. 

Why  the  tympanum  of  the  Parthenon  was  made  higher 
than  usual  may  be  accounted  for  in  various  ways.  Possi- 
bly it  was  in  order  to  accommodate  the  statuary  to  be 
placed  in  it.  Possibly  it  was  thought  that  if  the  raking 
cornice  and  cymatium  were  treated  in  the  general  scheme 
of  the  proportions  as  a border  above  and  aside  from  the 
tympanum,  while  the  latter  was  made  to  be  of  like  size 
with  the  whole  entablature,  this  arrangement,  on  account 
of  its  very  unusualness,  would  give  particular  emphasis 
to  the  statues.  Perhaps,  however,  it  is  more  consonant 
with  what  we  know  of  the  Greek  methods  to  suppose  that 
this  particular  pediment  was  made  higher  in  proportion 
in  order  that  it  might  not  appear  lower  than  that  of  the 
ordinary  temple.  The  Parthenon  itself  was  high — it  stood 
on  a hill ; it  was  impossible  to  look  at  it  from  any  position 
without  looking  upward.  (See  the  temple  at  the  right  in 
Fig.  95,  page  186.)  In  these  circumstances  the  heavy  pro- 
jecting cornice  over  the  entablature  would  necessarily  seem 
to  increase  the  height  of  the  entablature  and  at  the  same 


THE  PARTHENON. 


217 


time,  by  hiding  part  of  the  tympanum,  would  seem  to  les- 
sen the  height  of  the  pediment.  Very  likely,  too,  some 
of  the  outlines  of  the  statues  in  the  tympanum  would  aug- 
ment the  effect  of  lessening  its  apparent  height.  It  may 
be  that  both  in  this  temple  and  in  others,  in  which  we  find 
the  pediment  as  a whole  higher  than  the  entablature 
proper,  the  reason  is  the  same.  To  one  looking  upward, 
the  measure  of  the  space  given  to  the  entablature  extends 
from  its  base  diagonally  to  the  edge  of  its  cornice,  while 
that  of  the  tympanum  extends  upward  from  this  same 
edge  and  not  from  the  actual  bottom  of  the  tympanum, 
which  is  always  concealed.  Recalling  that  the  Greeks,  as 
will  be  shown  in  the  next  chapter,  always  determined  pro- 
portions, not  by  real  measurements,  but  by  apparent 
effects,  we  can  recognize  that  this  is  exactly  the  way  that 
they  would  treat  entablature  and  pediment  as  contrasted 
with  each  other. 

The  proportions,  each  to  each,  of  the  rectangles  formed 
by  the  width  and  height  of  the  three  spaces  occupied,  re- 
spectively, by  the  columns,  the  entablature,  and  the  pedi- 
ment of  the  Parthenon  will,  of  course,  seem  to  us  to  differ 
according  to  the  places  where  we  separate  them.  The 
breadth  of  this  temple  at  its  base  was  101.341.  Making 
allowance  for  the  diminution  of  this  breadth  above  the 
columns,  the  27.700  between  the  apex  of  the  pediment 
and  the  bottom  of  the  columns’  capitals,  would  be  to  the 
breadth  about  as  4 : 14,  of  which  the  height  of  the  space 
given  to  the  pediment  and  to  the  entablature,  each  re- 
spectively, would  be  as  2 : 14,  or  1:7.  The  rest  of  the 
front  down  to  the  bottom  of  the  stylobate  would  be  as 
5:  14,  both  together  9:  14.  Or  if  we  compare  the  rec- 
tangle enclosing  the  entablature  including  the  abacus, 
11.94,  with  that  enclosing  the  columns  under  it,  we  find 


218 


PROPORTION  AND  HARMONY. 


the  height  to  the  breadth  of  the  first  as  I : 9,  of  the  sec- 
ond as  3:9,  or  1 : 3,  and  of  both  together  as  4:  9 — -the 
same  numbers  used  by  Lloyd  (P.,  appendix,  page  112)  to 
represent  the  whole  breadth  and  length  of  the  building. 
If  to  this  we  add  the  rectangle  inclosing  the  tympanum, 
aside  from  the  pediment,  the  whole  is  as  5 : 9. 

It  may  be  well  to  notice  here  again,  in  passing,  that 
Lloyd  says  (P.,  appendix,  page  112),  that  the  hei  ght  of 
the  Parthenon  is  to  its  length  as  2 : 7,  and  that  the  same 
proportions  hold  good  of  the  temple  at  Bassse ; that  the 
height  of  the  former  temple  is  to  its  breadth  as  9:  14; 
that  the  same  dimensions  at  Bassse  and  in  the  Theseum 
and  west  front  of  the  Propylaea  are  as  3:4,  as  also  that 
the  Parthenon  has  breadth  and  length  as  4 : 9.  It  is  es- 
sential, however,  to  bear  in  mind  that  the  different  ways 
of  comparing  the  parts  or  wholes  of  heights  or  lengths  or 
breadths,  each  of  which  ways  reveals  the  appearance  of 
some  different  but  consistent  system  of  measurement,  are 
all  of  them  merely  the  necessary  and  inevitable  results  of 
applying  to  each  of  the  dimensions  that  are  brought  to- 
gether the  principle  of  making  them,  as  often  as  feasible, 
appear  to  be  alike,  or  to  be  divisible  by  like  factors.  Those 
who  hitherto  have  dwelt  upon  these  resulting  ratios  as 
though  they  were  the  main  things  to  be  considered,  have 
done  merely  what  so  many  others  have  done  before  them, 
namely,  taken  the  effect  for  the  cause.  See  page  152. 

Before  passing  from  these  Greek  temples,  it  is  well, 
perhaps,  to  point  out  that  often  the  front,  as  a whole, 
seems  to  have  been  constructed  upon  the  principle  of 
putting  a like  height  with  a like  breadth,  as,  for  instance, 
where  three  of  the  six  columns  with  the  two  spaces  be- 
tween them  constitute  an  exact  square.  This  arrange- 
ment is  emphasized  in  the  west  front  of  the  Propylaea 


COLUMNS  OF  GREEK  TEMPLES. 


219 


(see  the  middle  temple  in  Fig.  95,  page  186),  by  making 
the  space  between  the  two  central  columns  unusually 
wide,  thus  suggesting  at  once  the  way  in  which  the  three 
columns  on  each  side  of  it  are  grouped.  “ In  the  Par- 
thenon,” says  Lloyd  (P.,  appendix,  page  112),  “this  sym- 
metry is  applied  to  three  ordinary  columns  and  the  two 
intercolumns  included,  and  the  same  appears  to  be  the 
case  at  Sunium.  ...  In  the  temple  at  Rham- 
nus,  the  dimension  is  taken  from  the  outer  edge  of  the 
angle  column  to  the  centre  of  the  third  from  the  angle  ; 
in  the  Theseum  [Fig.  10,  page  36],  we  have  a like  divi- 
sion, but  involving  only  ordinary  columns.  I apprehend 
that  the  introduction  of  these  equalities  of  heights  with 
breadths  was  found  to  give  repose  to  the  effect  of  a long 
range  of  columns  as  a repetition  of  similar  spaces  and 
dimensions.”  This  seems  probable.  As  has  been  shown 
abundantly  in  this  discussion,  repetition,  or  rather  meas- 
urements that  gave  the  effect  of  repetition,  were  elements 
of  artistic  method  which  the  Greeks  seldom  neglected. 

They  also  made  the  breadth  of  the  column — usually 
calculated  from  the  abacus,  which  itself  was  equal  to  the 
lower  diameter — sustain  a certain  proportion  to  its  height. 
Lloyd  (P.,  appendix,  page  1 13)  says  that  at  Bassae,  in  the 
Theseum,  and  in  the  outer  columns  of  the  Parthenon,  the 
width  of  the  abacus  is  to  the  height  of  the  column  as  1 : 5. 
Vitruvius  tells  us  (“  De  Architectura,”  bk.  iv.,  chap,  i.)  that 
the  relations  in  a Doric  column  of  the  breadth  (Fig.  93,  page 
182)  of  the  base  to  the  height  represent  the  proportions  of 
a man,  i.e.,  of  the  length  of  his  foot  to  his  whole  height, 
viz.,  1:6;  the  proportions  of  the  Ionic  column  (Fig.  97, 
page  204)  represent  those  of  a woman,  viz.,  1 : 8,  but  later 
of  a Chinese  maiden,  perhaps  1 :g  and  also  I : 10. 

Thomson  says  in  his  poem  on  Liberty  : 


220 


PROPORTION  AND  HARMONY. 


First  unadorned 
And  nobly  plain  the  manly  Doric  rose  ; 

The  Ionic  then,  with  decent  matron  grace 
Her  airy  pillars  heaved  ; luxuriant  last 
The  rich  Corinthian  spread  her  wanton  wreath. 

It  yet  remains  for  us  to  show  how,  by  actual  measure- 
ments, the  statements  under  the  headings  IV.,  page  195, 
and  V.,  page  198,  can  be  verified,  and  made  applicable  to 

all  the  Doric  temples  of  which 
we  have  records.  Fortun- 
ately Hittorf  repeats,  accord- 
ing to  his  system,  the  meas- 
urements of  the  temples  of 
zEgina  and  Bassae,  and  in  the 
Theseum  and  Parthenon. 
With  what  we  have  learned 
about  these  from  the  more 
detailed  measurements  of 
Penrose  and  Cockerill,  it  will 
be  easy  to  recognize,  and  be 
logical  to  infer,  that,  in  the 
fig.  98.  other  temples,  like  measure- 

corinthian  capital  of  pillar.  ments  exemplify  like  princi- 

See  pages  203,  220.  , 0 

r b pies,  bee  page  221. 

It  is  not  necessary  to  pursue  this  subject  further. 
There  are  many  Ionic  and  other  temples,  gateways,  and 
monuments,  the  drawings  of  which,  in  the  superficial  way 
in  which  they  must  be  judged  in  the  lack  of  exact  meas- 
urements, reveal  the  application  of  the  same  principles. 
But  it  would  not  accord  with  the  design  of  this  essay  to 
consider  such  forms  of  testimony  here.  Besides,  it  is  un- 
necessary. Everyone  admits  that  the  Doric  style,  espe- 
cially in  the  temples,  represents  Greek  architecture  in  its 


MEASUREMENTS  OF  GREEK  TEMPLES. 


221 


H 

X 

0 


£ 

X 


Whole 
Space 
above  to 
Col.  Space. 

u u 

0 0 

m s«  <0  MroHMM  fo  M rt  ro  « m n co  m 

mvOCONVOCONmmwm  m N m m m N « N M h N m N m 

Ped.  or 
Length- 
ened Ent. 
to  Short- 
ened Col. 

OO  O 

cs  t^oo  co  t^co  co  pj  n n p*  n n n n n ffj  ro  fo  n rt- fC)  cocon 

MCOCOmCOCOH  M M M M MMHMM  M M M 

Column 

without 

Cap. 

^'O  . ^ 

.3  C i/i  3 (/)  1) 

VO  10  -t-  TMrt  com  0 rt  3 O'  N O co  m 03  ON-fOOco  — . VO  0 N 

too  S'  mmifiTf  3 _ ’fO'iriHrt-i.n  - s.  ioco  O -j-  0 — ; coo  m 

vo  vo  co  t>.oo  q -f;  _2  c3  00  00  00  q"q  -£j  ^ m rc,  a n m co  .3  0 vq  co  10 

•4-10  O'  co  4co  vd  r O-2  co  cn  n n m r ^3  in  d in  d 6 0 'td’N 

- ?<  " h » n ^ 

Half  of 
Latter. 

O t".  10  0 00  n vo  MO'-'i-oO'  coh  novo  m co  tovo 

n to  O'  h mss  n o>  'f  ci  vo  t^co  000  0 10  co « vo 

coo  q h toms  O'  n 0 0 S'  O'  000  vo  co  m co  0 

Pi  N 4 4 S'  4 pi  H H 4 4 ci  H 4 M cn  « (N  M CO  CO 

Ped. and 
Ent.  with 
Cap  of 
Col. 

0 0 l/J  (/)  0 

m -t  0 SvVO  -rt-  <N  JZ  V-1  hf)  co  OO  O'  O OO  _C  3 S*NIO0Nm.C  . SM  N 

o>  coHTj-m  “O.Jr  ^ O' 00  tj-  co  *->  u -^-vo  0"0  O'M  vo  m co 

vq  m m N.  ^ H.  > ”o  « •-  °o  vo  q q vq  ^ rt  °'0'c!'^c?t>  s c.9  «q  q> 

4 -4-  co  co  4 O'  10  >rj^  co  pi  00  cc  in  ^ coco*  coNinin  ? pIio  n 

m 0 ^ H z 

Cap  of 
Column. 

0.629 

0- 543 

0.860 

0.756 

1- 474 
I-334 
0.668 

Abacus 
and  Ovolo 
of  Cap. 

0.251 

0.308 

0.882 

0.710 

0-594 

Abacus. 

0.199 

0.329 

0.195 

0.420 

0.260 

0.853 

Archi- 
trave and 
Frieze. 

00  10  co  to  « 0 Oco  00  m co  O'  0 cooo  S'  -t-vo  co  0 

O'  O O'  O N lO  M to  P'VO  Tj-  10  SM  in  t-'VO  to  to  O'VO  M 0 

vo  vo  vo  MN-rt-M  >—  M OO  N M vo  covo  OHIO  NCO  O'lOO' 

mm  in  covd  cod  m m pi  co  n m co  m co  ei  vo’  mnnmm 

Entabla- 
ture as 
Usually 
Measured. 

NM  S'  m N O S*  NO  VOCO  tt-  SlOCvO  N M o to  N M Q 

S'  O'  M VO  rj-  M N VO  CO  VO  lO  O'  S>  CO  t IOO  CO  N 00  O'  O'  O 

O oo  co  q>  oo  toco  co  covo  n S'  O' co  o O inov  mmo  Nt 

N M co  COVO  4 pi  M M CO  4 pi  M m P)  4 P)  N M CO  4 m"  pi 

Pediment 

as 

Usually 

Measured. 

OO  CO  0 Q Q S'  OONNO  M'J-OOOO  t^vo  o • • 

■rt-oo  M NOOio  fOH  tsin  st  O O'COCO  0"0  -t-  - . 

O'  V O O'  vo  t CO  o N O'  »n  O M t^vo  S«VO  O'  ts  OCO  • • 

MM  CO  covo’  CO  pi  M O co  CO  ci  MCOMCONVO  6 co  CO  i I 

Column. 



>n  co  -rt-  O O S CO  O O N co  to  OvtO  O 0>0  VO  VO  N O o 

CO  -t-  CO  «NOOM  o O CO  N CO  o COtOVO  Ol  covo  M o O 

n O'  -t-  >-  n m mn  t^vo  n S'  O'  m n co  m mcompi  t 

vo  in  o O'VO  6 vo  ■’t  4 CO  covo  to  O vo  M*  o’  4 4 O'  S'  to  VO 

c g 

"So  cq 

S3  n 


tp 

bO 

< 

||| « 
'3l3'«T3 
cflWW  O 
d G 

CO  H pi  6 


e 3 £ 

111 

«Ph  3 3 
fi«  n!  C C 
rt  U3G 
.2  w c u ^ 
</>•«  Sc/2c/3 
22  fc  ~ « 

c w art  t« 
<u  -C  <u  . . 

^H2U< 


£ 2 

ag 

•S  § 1 6 
w « - s 

: 4-.  n!  G rt 


J2  g.S*5.’a! 

, w »-i  3 3 •• 

HuS  *— ■ >—£ 


QinQCuS 


5.644  H.,  probably  3.644. 


222 


PROPORTION  AND  HARMONY. 


prime  ; and  only  in  its  prime  is  it  important  for  us  to 
study  it.  It  must  be  borne  in  mind,  too,  that  the  object 
of  our  inquiries  has  been  to  ascertain  the  general  princi- 
ples in  accordance  with  which  the  Greek  builder  worked, 
not  his  special  applications  of  them.  Nor  are  these  prin- 
ciples necessarily  invalidated  merely  because,  in  some 
temples,  the  ratios  that  have  been  mentioned  do  not  seem 
to  be  indicated  as  unmistakably  as  is  desirable.  All  that 
is  necessary  is  that,  as  in  the  case  of  the  Parthenon,  there 
should  be  evidences  of  some  scheme  or  schemes  of  ratios, 
indicative  of  like  subdivisions. 

Of  the  existence  in  all  these  temples  of  some  such 
scheme,  we  may  be  certain.  Every  list  of  figures  that  we 
have  found  proves  it.  The  Greek  builder  was  careful  to 
preserve  the  appearance  of  putting  like  dimensions  with 
like.  And  this  fact  was  probably  the  cause  not  the  result 
of  whatever  proportions  his  buildings  manifested.  If,  in 
time,  laws  like  those  mentioned  by  Vitruvius  arose,  it  is 
more  than  likely  that  most  of  these  in  the  forms  in  which 
they  have  been  preserved,  were  after-thoughts,  derived 
from  what,  at  a period  when  architecture  was  no  longer  in 
its  prime,  was  discovered  by  measuring  the  buildings  of  the 
fathers.  Why  it  should  ever  have  passed  its  prime  and 
begun  to  decline  is  easy  to  perceive.  When  any  form  of 
art  is  young,  men  are  never  tired  of  going  back  to  first 
principles  and  experimenting  with  their  designs,  not  only 
in  painting  and  sculpture  but  in  architecture  too,  just  as 
often  as  effects  seem  unsatisfactory.  See  what  is  said  fur- 
ther upon  this  subject  on  page  300.  After  the  earlier, 
creative  periods  of  the  art,  however,  men  begin  to  think 
that  the  whole  subject,  and  all  its  methods,  have  been 
mastered.  They  imagine  that  no  more  practical  experi- 
ments are  needed.  They  are  first  contented  with  what 


FIG.  99.— PANTHEON,  ROME. 


224 


PROPORTION  AND  HARMONY. 


has  been  achieved  by  their  ancestors,  and  then  they  begin 
to  have  a traditional  veneration  for  it.  That  which  should 
stimulate  them  to  thought,  stirs  them  only  to  reverence, 
and,  like  many  of  the  critics  and  architects  of  our  own 
day,  they  come  to  teach  in  their  schools,  and  to  believe 
in  their  hearts,  that  to  be  a successful  imitator  is  to  em- 
body the  only  praiseworthy  artistic  ideal.  Undoubtedly 
this  was  the  fate  that,  after  a time,  overtook  the  architects 
of  Greece.  They  became  imitators.  Because  their  copies 
stood  before  them,  they  ceased  to  experiment.  Because 
they  did  not  need  to  conceive  their  own  designs  they 
ceased  to  think  about  them  ; and  when  they  ceased  to  do 
this  they  necessarily  ceased  to  cause  them  to  develop, 
and  began  to  cause  them  to  deteriorate. 

Before  long,  they  began  to  regard  as  ends  those  meth- 
ods which  the  great  architects  had  used  as  means.  They 
reproduced  the  subordinate  features  in  the  older  temples, 
but  overlooked  the  principal  ones.  Finally  all  the  meas- 
urements that  they  used  grew  discordant,  and  it  was  be- 
yond the  power  of  any  rules  like  those  of  Vitruvius  to 
make  them  otherwise.  Columns,  entablatures,  and  tym- 
panums, bore  a general  resemblance  to  those  upon  the 
Acropolis,  but  contained  not  one  element  that,  in  the  es- 
timation of  the  merest  tyro  of  the  art,  could  entitle  them 
to  be  considered  architectural  models.  Compare  the 
front  of  the  temple  in  Atgina  or  of  the  Theseum,  Figs.  10, 
page  36,  and  94,  page  183,  with  that  of  the  Pantheon  of 
Rome,  Fig.  99,  page  223,01-  of  St.  Paul’s,  Covent  Garden, 
London,  Fig.  100,  page  225.  Could  any  building  be  more 
completely  caricatured  than  is  each  of  the  Greek  ones  by 
either  the  Roman  or  the  English  imitation  ? 

What  makes  the  difference  between  these  buildings? 
Look  at  them.  The  Greek  temples  emphasize  results, 


IMITATION  OF  GREEK  PROPORTIONS. 


225 


which  the  others  do  not,  attained  by  putting  like  with  like. 
All  the  best  Greek  buildings  show  similar  effects,  and  why  ? 
Because  the  Greek  lived  near  to  nature.  His  buildings 
emphasized  corresponding  measurements  for  the  same 
reason  as  the  card  houses  of  a child.  The  Greek  carried 
out  the  instinctive  promptings  and  prescriptions  of  the 
mind.  It  was  in  the  endeavor  to  do  this  that  he  originated 
those  scientific  adjustments  to  accommodate  actual  pro- 
portions to  optical  requirements,  which  will  be  considered 


FIG.  100.— ST.  PAUL’S,  COVENT  GARDEN,  LONDON. 

See  page  224. 


in  the  following  chapters.  Only  much  later  did  this  end 
absorb  the  whole  interest  of  builders,  as  it  has  that 
of  modern  students  who  have  examined  their  works,  and 
thus  divert  attention  from  more  important  matters  on 
account  of  which  alone  these  optical  requirements  were 
at  first  studied.  The  result  was  on  a par  with  that  of 
the  exclusive  attention  paid  to  the  secondary  details  of 
poetic  form  in  the  time  of  Queen  Anne,  leading  to  the 
pompous  prosaic  jingle  that  during  most  of  the  last  cen- 
tury passed  in  England  for  the  only  permissible  poetic 
phraseology. 

As  has  been  pointed  out,  the  proportions  of  the  Parthe- 
non are  more  intricate,  and  the  recognition  of  them 

more  difficult  than  in  earlier  buildings.  So  while  it  re- 
15 


226 


PROPORTION  AND  HARMONY. 


presents  the  highest  achievement  of  Greek  architecture,  it 
also  represents  the  beginning  of  its  decline.  Subsequently 
men  came,  more  and  more,  to  forget  to  have  their  designs 
manifest  clearly  the  results  of  relative  measurements. 
Gradually  they  became  accustomed  to  see  buildings  in 
which  such  requirements  were  disregarded.  But  study  will 
show  that  at  the  time  of  the  Gothic  and  the  Renaissance 
revivals,  the  manifestation  in  buildings  of  the  principle  of 


FIG.  101.— OLD  PICTURE  OF  ST.  SOPHIA,  CONSTANTINOPLE. 
See  page  226. 


putting  large  numbers  of  like  dimensions  with  like,  again 
came  to  be  considered  necessary.  See  Figs,  n,  page  37; 
12,  page  38  ; 76,  page  147;  81,  page  155  ; 86,  page  167,  and 
IOI.  It  is  considered  so  in  all  great  architecture. 

In  case  our  own  builders  ignore  this  fact,  we  can  ex- 
pect but  little  from  them.  They  may  turn  out  of  their 
planing  mills  or  stone  quarries,  pillars  that  look  like  those 
of  Greek  temples,  or  arches  that  look  like  those  of  Gothic 
cathedrals ; they  may  discard  these  older  models  al- 


MODERN  ARCHITECTURE. 


227 


together,  and  try  as  hard  as  savages  to  be  original  by 
bringing  together  discordant  mixtures  of  shapes,  sizes, 
styles,  and  colors,  and  doom  to  eternal  infamy  the  names 
of  Queens  Anne  and  Elizabeth  by  calling  their  hotch-potch 
after  them  ; but  no  great  architecture  or  school  of  archi- 
tecture can  be  produced  in  this  way.  Great  architecture  is 
founded  upon  principles  that  are  in  the  constitution  of 
nature  and  of  mind,  the  applicability  of  which  all  men 
recognize.  Nor  can  they  be  ignored  or  neglected  in  any 
product  of  art  without  lessening  the  force  of  its  appeal  to 
human  interest. 

As  has  been  suggested,  proportion,  in  its  character, 
is  not  only  simple  but  complex,  and  its  effects  cannot 
be  produced  on  a large  scale  without  the  most  careful 
and  profound  study.  These  effects,  too,  are  still  capable 
of  further  development.  The  forms  of  Greek,  Gothic, 
Moorish,  Romanesque  or  Renaissance  art  have  no  more 
exhausted  the  possibilities  of  architecture  than  analogous 
developments  in  poetry,  painting,  or  music.  In  this  land 
and  age,  we  can,  and  should,  have  an  architecture  of  our 
own,  to  meet  the  requirements  of  our  climate,  as  the 
Greek  may  not ; of  our  customs,  as  the  Gothic  may  not ; 
and  of  our  artistic  instincts,  as  the  Queen  Anne  may  not. 
Such  an  architecture  can  be  thoroughly  original,  yet  if,  in 
trying  to  make  it  so,  we  neglect  the  principles  according 
to  which  the  minds  that  are  to  view  it  must  judge  of  it, 
we  cannot  expect  it  to  commend  itself  to  general  approval, 
even  in  our  own  times,  and  much  less  in  coming  times. 
Whatever  may  be  the  nature  of  his  designs,  the  architect 
who  deals  with  shapes  must  remember  that  shapes  fill 
space  just  as  sounds  fill  time,  and  that  for  the  purposes 
of  art  the  appearances  of  similarly  related  measurements 
in  the  one  are  as  necessary  as  in  the  other.  In  short,  he 


228 


PROPORTION  AND  HARMONY. 


must  never  forget  that  which  it  has  been  found  necessary 
to  repeat  so  many  times  already,  that  the  fundamental 
principle  in  art  is  to  group  sizes  as  well  as  shapes  by  put- 
ting together  those  that,  if  not  in  wholes,  in  parts  at  least 
can  be  made  to  seem  alike. 


CHAPTER  XIV. 


HARMONY  OF  OUTLINES  : PERSPECTIVE. 

Outlines  and  Colors,  the  Respective  Analogues  of  Words  and  Tones — Form- 
Harmony  is  less  Essential  than  Significant  Representation,  yet  Im- 
portant— In  Poetry  Harmony  is  Owing  to  Apparent  Like  Effects  as  in 
Alliteration,  etc.,  and  also  to  Subtle  Effects  Adapted  to  Ease  of  Audi- 
tory Action — Analogous  Conditions  in  Arts  of  Outline  : The  Perspective 
and  Circumspective — Perspective  Relates  all  Objects  to  a Centre  of  the 
Field  of  Sight  : Lines,  Directed  toward  this  Centre,  Converge — Appear- 
ance of  Horizontal  Lines — Of  Vertical  Lines — Both  Lines  as  Repre- 
sented in  Painting  and  Architecture— Optical  Illusions  in  Triangles — 
In  Horizontal  with  Crossing  Vertical  Lines — Exact  Explanation  of 
these  Illusions  not  as  Important  as  to  Recognize  that  they  Exist — An- 
alogy Drawn  from  Effects  of  Color  Remote  and  Near — Failure  in  our 
Time  to  Recognize  the  Fact  as  -Applied  in  Architecture — A Building 
was  once  Judged  by  its  General  Effect  as  Seen  from  a Distance — Proof 
of  this  Furnished  by  Discoveries  in  Egypt  and  Greece  by  Pennethorne, 
Hofer,  Schaubert,  and  Penrose — By  Goodyear — His  Special  and  Gen- 
eral Contribution  to  the  Subject— Some  Measurements  of  Penrose — To 
be  Interpreted  as  Related  to  Perspective,  not  to  Proportion — Differ- 
ences in  Measurement  Accord  with  this  Interpretation— Greek  Archi- 
tects Experimented  with  their  Products  as  Artists  do  in  other  Arts. 

''J'' HE  harmony  of  outline  seems  related  to  that  of  color 
precisely  as  the  harmony  of  words  is  related  to  that 
of  musical  tones.  In  using  words,  as  also  outlines,  the 
primary  consideration  is  their  significance,  a requirement 
mainly  psychological,  depending  upon  the  definiteness  of 
the  effect  produced  by  a form  as  a whole.  In  using  musi- 
cal tones,  as  also  colors,  the  primary  consideration  is 
harmony  of  effect,  a requirement  mainly  physiological, 
produced  by  the  methods  of  blending  together  the  differ- 


229 


230 


PROPORTION  AND  HARMONY. 


ent  factors  of  the  form.  But  while  this  is  true,  it  is  also 
true  that  the  harmonious  arrangement  of  words  and  of 
contours,  though  secondary,  is  extremely  important,  just 
as  is  definiteness  of  significance  in  tones  and  tints.  It  is 
with  the  methods  through  which  outlines  may  be  made 
to  conform  to  the  physiological  requirements  of  harmony, 
that  we  are  to  deal  in  this  chapter. 

In  Chapters  VII.  to  XII.  of  “ Rhythm  and  Harmony  in 
Poetry  and  Music  ” it  was  said  that,  in  order  to  produce 
harmony,  the  tones  of  speech  never  have  been,  and  never 
need  be,  selected  and  arranged  as  in  musical  scales  or 
chords.  Speech  may  use  any  tone  that  can  be  uttered,  so 
long  as  it  is  appropriate  for  definite  reference.  Neverthe- 
less, in  artistic  speech,  as  in  poetry,  the  harmonic  ratios 
that  underlie  musical  pitch  are  often  exactly  though 
subtly  reproduced.  At  the  same  time,  the  poet  who  re- 
produces them  successfully,  does  not  do  so  directly,  i.  e., 
by  thinking  of  the  pitch  of  his  tones  while  he  is  composing. 
He  does  so  indirectly,  i.  e.,  while  thinking  merely  of  ac- 
commodating the  sounds  to  the  physiological  require- 
ments of  the  ear;  so  that,  as  the  tones  pass,  the  one  into 
the  other,  they  shall  produce  a satisfactory,  agreeable,  and 
artistic  effect;  in  other  words,  so  that  the  transitions  shall 
seem  not  sharp  and  abrupt,  but  smooth,  euphonious,  and 
natural.  In  order  to  attain  this  end,  poets  use  such 
methods  as  in  the  repeated,  or  regularly  recurring  sounds 
in  alliteration,  assonance,  and  rhyme,  or  in  the  very  easily 
coalescing  sounds  in  phonetic  syzygy  and  gradation, — 
all  of  which,  as  shown  in  Chapters  VII.  to  XII.  of 
“ Rhythm  and  Harmony  in  Poetry  and  Music,”  are  de- 
velopments, in  as  true  a sense  as  are  the  harmonics  of 
music,  of  the  principle  of  grouping  complex  wholes  through 
putting  together  those  that  have  like  partial  effects. 


EASE  OF  OCULAR  ACTION. 


231 


So  in  the  arts  of  outline.  What  the  artist  successful  in 
these  thinks  of,  is  the  method  of  accommodating  their  ap- 
pearance to  the  physiological  requirements  of  the  eye  so 
that  they  shall  have  satisfactory,  agreeable,  and  artistic 
effects.  How  can  they  be  made  to  have  these  ? How  but 
by  being  made  to  pass  into  one  another  so  as  to  require, 
in  the  whole  eye  or  in  different  parts  of  the  eye  when  re- 
garding them,  the  least  possible  effort,  or  conflict  between 
different  tendencies  of  effort  ? Exactly  what  this  means, 
will  be  understood  when  it  is  recalled  that  the  eyes,  in  com- 
paring together  and  uniting  part  after  part  of  the  field  of 
sight,  are  almost  constantly  moving  upward,  downward, 
and  sideward,  as  well  as  changing  divergence,  convergence, 
focus,  axis,  and  lens.  See  Fig.  1 14,  page  273.  With  these 
conditions,  it  is  needless  to  argue  that,  as  a rule,  the  least 
possible  effort  of  this  kind  is  required  where  outlines  in- 
volve some  form  of  repetition.  When  we  are  using  a 
phrase  like  “ Many  men  of  many  minds,”  though  the  un- 
accented syllables  differ,  the  fact  that  the  organs,  being 
once  arranged  for  the  z/z-sound  in  the  accented  syllables, 
regularly,  when  these  recur,  return  to  this  same  position, 
makes  the  utterance  easy.  So  the  regular  repetition  in  a 
building  of  like  pillars  or  openings,  as  in  windows  or  doors, 
makes  it  easy  for  the  eye,  as  well  as  mind,  to  take  in  the 
whole  ; just  as  irregularity,  or  the  absence  of  repetition — 
pillars,  windows,  doors,  all  of  different  shapes  and  sizes — 
causes  a confused  effect,  and  makes  an  appearance  difficult 
for  the  eye  to  take  in.  Ease  of  ocular  action,  therefore, 
may  be  said  to  attend  upon  repetition.  If  so,  it  must  at- 
tend, in  some  degree,  upon  partial  repetition  also,  as  in 
balance , alternation , consonance , and  interchange , or  any  of 
the  methods  indicated  in  the  chart  on  page  3.  Exactly 
why  this  should  be  the  case,  is  fully  discussed  in  what  is 


232 


PROPORTION  AND  HARMONY. 


said  of  shapes  and  outlines  in  “ The  Genesis  of  Art-Form.” 
In  this  place,  it  is  necessary  to  consider  only  a more  subtle 
phase  of  the  subject.  This  has  to  do  not  with  the  mere 
repetition  or  recurrence  of  the  same  forms  of  lines,  but 
with  that  which  underlies  such  effects,  and  renders  them 
important,  namely,  the  repetition  or  recurrence  of  the 
same  forms  of  ocular  action.  Chapters  VI.  to  XII.  of 
“ Rhythm  and  Harmony  in  Poetry  and  Music  ” show  that, 
as  elements  of  harmony  in  poetic  verse,  we  have  to  con- 
sider not  only  actual  repetitions,  as  in  the  like  sounds  in 
alliteration,  assonance,  and  rhyme,  but  also  effects  pro- 
duced by  combinations  or  successions  of  vowels,  conso- 
nants, and  syllables,  when  easily  coalescing.  In  these 
effects,  the  associated  sounds  are  not  as  nearly  alike  as  in 
alliteration  or  assonance,  but  they  are  allied  ; and  are  ar- 
ranged in  such  ways  as  to  necessitate  as  little  effort  as  is 
compatible  with  any  change  at  all  in  the  organs  while  ut- 
tering them,  either  actually,  as  when  reading  aloud  ; or 
imaginatively,  as  when  reading  to  oneself.  Of  course, 
outlines  can  be  arranged  in  ways  corresponding  to  this. 
They  are  so  arranged,  for  instance,  when  they  are  ad- 
justed in  such  ways  as  to  accommodate  themselves  to  that 
which  can  be  seen  at  a single  glance  from  a single  view- 
point, and  therefore  without  any  change,  at  least  any  con- 
scious change  (see  page  271)  in  the  axis,  focus,  or  lens  of  the 
eye.  This  condition  involves  a fulfilment  of  what  is 
termed  the  principle  of  perspective  ; and  it  may  be  said  to 
correspond  to  such  verse-effects  as  are  most  nearly  con- 
nected with  actual  repetition  (see  chart  on  page  3).  Again, 
outlines,  or  those  parts  of  them  nearest  to  one  another, 
may  be  said  to  be  arranged  according  to  the  requirement 
just  indicated,  when  they  are  adjusted  in  such  ways  that 
straight  lines  are  made  to  pass  into  curves,  or  curves  of 


PERSPECTIVE. 


233 


one  kind  into  those  of  another  kind,  by  regular  degrees  of 
change.  This  method,  as  distinguished  from  the  perspec- 
tive, which  means  literally  looking  through  a scene,  one  is 
tempted,  coining  a word  or  rather  a new  application  of  an 
old  word,  to  call  the  circumspective , which  means,  literally, 
looking  around — looking  around  the  sides  or  extremities 
of  an  object,  or  at  its  surroundings.  According  to  this 
method,  though  there  may  be  conscious  changes  in  axis, 
focus,  or  lens,  as  the  eyes  look  from  one  line  or  part  of  a 
line  to  another,  the  changes  are  as  slight  as  possible,  and 
occur  by  regular  degrees — in  these  regards  evidently  pro- 
ducing effects  corresponding  to  those  of  verse  which  are 
most  nearly  connected  with  phonetic  gradation.  See 
chart  on  page  3,  also  Chapter  XI.  of  “ Rhythm  and  Har- 
mony in  Poetry  and  Music.” 

Of  these  two  methods  of  producing  harmony  of  outline, 
let  us  first  consider — of  course  only  so  far  as  is  necessary 
for  our  present  purpose— the  one  concerning  which  the 
most  is  known,  and  can  be  said, — namely,  perspective. 
Of  this,  the  essential  fact  interpreting  all  its  phenomena 
is  that,  owing  to  the  effect  of  distance  upon  the  eyes, 
all  objects  perceived  by  them  are  related  to  a centre  of 
the  field  of  vision,  about  which  centre  every  line  has  a 
tendency  to  appear  either  to  radiate  or  to  form  a circum- 
ference. Let  us  apply  this  fact  first  to  lines — and  here 
we  need  to  consider  only  straight  lines — extending  in  the 
same  direction  as  the  glance  of  the  eye  regarding  them. 
These  lines,  though  in  nature  they  may  be  parallel,  are 
never  parallel  in  the  image  of  which  we  are  conscious  on 
the  retina,  and  which,  as  must  always  be  borne  in  mind,  is 
the  model  for  imitation  in  art.  They  converge  toward  a 
vanishing-point  as  it  is  termed,  where,  in  the  extreme  dis- 
tance, they  apparently  meet.  See  the  left  upper  corner  of 


234 


PROPORTION  AND  HARMONY. 


Fig.  102,  page  235.  They  converge  thus,  of  course,  be- 
cause the  spherical  shape  of  the  eye  causes  the  lines  or 
axes  of  vision  as  they  extend  outward  to  radiate,  and 
thus  to  render  visible,  when  far  enough  away,  not  only  an 
object  which  is  exactly  in  front  of  the  eye,  but  also  much 
that  is  on  both  sides  of  this  object.  (See  Fig.  4,  page  22, 
also  Fig.  1 13,  page  272).  But,  for  this  reason,  anything 
held  within  a foot  or  two  of  the  face  may  appear  as  wide  as 
the  whole  field  of  sight  appears  at  the  horizon,  a stick  three 
feet  long  measuring  as  much  when  near,  as  does  a reach  of 
country  three  miles  long  when  at  a distance.  But  at  this 
distance,  an  object  three  feet  long  would  be  indistinguish- 
able, which  is  the  same  as  to  say  that  at  this  distance 
straight  lines  drawn  from  the  two  extremities  of  this  ob- 
ject as  held  immediately  in  front  of  the  eyes,  would 
appear  to  meet. 

Now  let  us  apply  what  has  been  said  of  objects’  being 
related  by  the  eye  to  a centre  of  the  field  of  vision,  to 
lines — and  here  again  we  may  confine  consideration  to 
straight  lines — extending  in  a direction  different  from  the 
glance  of  the  eye,  i.  e.,  to  lines  crossing  the  field  of  vision 
horizontally  or  vertically.  It  will  be  found  that  only  when 
lines  horizontal  in  nature — i.  e.,  parallel  to  the  earth’s  level 
— are  on  an  exact  level  with  the  eyes,  are  they  necessarily 
horizontal  in  the  image  of  which  we  are  conscious  on  the 
retina  ; and  only  when  lines  vertical  in  nature — i.  e .,  per- 
pendicular to  the  earth’s  level — are  directly  in  front  of 
us,  are  they  necessarily  vertical  in  this  image.  Horizontal 
lines,  if  above  the  level  of  the  eye,  will,  at  the  place  directly 
in  front  of  us,  curve  upward  in  the  image.  The  circum- 
ferences of  the  dotted  circles — not  of  the  inside  undotted 
one — surrounding  the  man  in  Fig.  103,  page  236,  represent 
— though,  for  the  purpose  of  illustration,  in  an  exaggerated 


< U~J 


236 


PROPORTION  AND  HARMONY. 


way — the  direction  of  lines  that  appear  to  him  to  be  hori- 
zontal. Evidently,  in  the  degree  in  which  he  gazes  up- 
ward, each  of  these  lines  above  him  will  describe  more 
and  more  of  a curve.  In  Fig.  81,  page  155,  the  summits 


FIQ.  103.— GREEK  TEMPLE  INSCRIBED  IN  CIRCLES  REPRESENTING  HORIZON  LINES. 

See  pages  234,  237,  239,  251,  255,  257,  258. 

of  the  two  steeples  are  on  a level.  A line  drawn  from  one 
to  the  other  is  that  which  represents  the  horizontal ; but 
notice,  if  actually  drawn  between  them,  what  a sharp  curve 
it  would  necessitate. 


PERSPECTIVE  IN  VERTICAL  LINES. 


23  7 


The  principle  of  perspective  as  applied  to  vertical  lines 
is  more  complex.  In  one  regard,  however,  it  corresponds 
to  that  which  is  true  of  horizontal  lines.  If  the  railway 
tracks  represented  in  the  upper  left  drawing  in  Fig.  102, 
page  235,  ran  up  a steep  hill,  or  even  a perpendicular  hill, 
they  would  continue,  as  they  do  now,  to  approach  one 
another.  In  other  words,  in  extreme  distance,  two  par- 
allel vertical  lines,  the  one  to  the  right,  and  the  other  to 
the  left  of  the  perpendicular  in  front  of  us,  incline  toward 
each  other.  See  this  vertical  effect,  purposely  exagger- 
ated, in  the  sides  of  the  temple  in  Fig.  103,  page  236. 
Compare  also  the  horizontal  distance  between  the  two 
towers  in  Fig.  81,  page  155,  at  their  bases,  and  at  their 
summits  ; also  the  decided  leaning  toward  the  central  per- 
pendicular of  the  field  of  sight  of  the  tower  of  St.  Mark’s 
which  rises  at  the  right  of  the  reproduced  photograph  in 
Fig-  31,  page  88,  of  “The  Genesis  of  Art-Form.”  Un- 
doubtedly, too,  could  we  perceive  straight  lines  drawn 
from  the  horizon  to  the  zenith,  those  on  each  side  of 
the  perpendicular  in  front  of  us  would  seem  to  meet  en- 
tirely, as  well  as  to  describe  slight  curves.  So  much  with 
reference  to  the  appearance  of  vertical  lines,  if  at  a dis- 
tance and  rising  to  extreme  height.  But  it  is  important, 
in  connection  with  them,  to  have  attention  directed  to 
the  fact  that,  if  these  lines  are  near,  or  rise  but  little  above 
the  horizontal  level,  their  appearance  is  determined  by  an 
entirely  different  principle,  which  has  an  exactly  opposite 
effect.  The  principle  is  derived  from  the  fact  of  the  rota- 
tion of  the  eyes.  They  rotate  whenever  the  axes  of  the 
two  eyes  converge—/,  e.,  whenever  in  order  to  see  distinctly 
and  specifically,  as  distinguished  from  indistinctly  and 
generally,  the  two  eyes  move  away  from  each  other — not 
toward  each  other,  as  some  might  suppose,  forgetting  that 


238 


PROPORTION  AND  HARMONY. 


the  lines  of  vision — i.  e.,  the  axes — of  the  two  eyes  cross  in 
passing  outward  (Le  Conte’s  “ Sight,”  p.  203).  The  eyes 
rotate  thus,  not  only  when  moving  apart  to  look  fixedly 
at  the  scene  in  front,  but  when,  moving  in  the  same 
direction,  both  are  glancing  from  side  to  side  of  this  scene. 
But  now,  when  the  eyes  rotate,  what  must  be  the  effect? 
What  but  to  cause  each  eye  to  roll  not  only  sideward 
but  also  downward  ? And  when  this  has  been  done  what 
should  we  expect  but — to  describe  the  result  more  graph- 
ically than  scientifically — that  each  eye  should  turn  the 
vertical  lines  at  one  side  of  the  field  of  sight  slightly  away 
from  the  perpendicular?  As  shown  by  a series  of  experi- 
ments in  chapter  i.  of  part  ii.  of  Le  Conte’s  “ Sight,”  this 
is  exactly  what  does  happen  ; in  the  resultant  image  on 
the  retina  formed  by  the  combined  action  of  both  eyes 
(see  what  is  said  of  binocular  vision  in  Chapter  XVI.), 
the  vertical  lines,  as  they  rise  at  the  sides  of  the  field  of 
sight,  seem,  immediately  above  the  horizontal  level,  to 
incline  slightly  away  from  the  perpendicular  in  front  of 
us.  Nevertheless,  at  a comparatively  short  distance  above 
this  level,  in  accordance  with  the  effect  of  the  altogether 
different  principle  determined  by  distance  or  perspective 
which  has  already  been  pointed  out,  these  same  vertical 
lines  seem  to  incline  toward  the  perpendicular.  It  will  be 
noticed,  however,  that,  as  applied  to  the  horizontal  lines 
above  the  level  of  the  eyes,  though  less  to  those  below  it, 
this  rotary  action  does  not  change,  but,  if  anything,  aug- 
ments the  effect  of  the  upward  curve  described  in  the  last 
paragraph. 

The  fact  just  mentioned  with  reference  to  the  side  verti- 
cal lines,  as  well  as  the  very  slight  effect  which,  when  very 
near,  is  exerted  upon  them  by  the  principle  of  perspective , 
justifies  painters  in  not  inclining  toward  the  perpen- 


PERSPECTIVE  IN  ARCHITECTURE. 


239 


dicular,  at  the  centre  of  the  field  of  sight,  trees  or  other 
objects,  if  of  no  great  comparative  height,  even  when  rising 
at  the  extreme  sides  of  their  pictures.  Moreover,  the 
subtle  curves,  not  only  in  the  vertical  lines  but  even  in 
some  of  the  horizontals,  are  comparatively  so  slight  that 
in  painting  they  need  not  often  be  given  consideration. 
But  in  architecture,  where  the  products  fill  a large  space 
in  the  field  of  view,  it  is  a question  whether  the  conditions 
of  nature  just  indicated  can  be  disregarded  without  artistic 
detriment.  Consider,  for  instance,  the  uses  of  the  hori- 
zontal line.  In  nature,  from  which  we  get  our  conception  of 
this,  it  represents  a level  every  part  of  which  is  equally 
distant  from  the  centre  of  a globe.  Such  a line  is  never 
really  straight.  It  is  really  curved  ; and  if  a horizontal 
line  be  far  enough  away  from  us  to  be  seen  for  a long  dis- 
tance, which  mainly  happens,  of  course,  when  it  is  above 
us,  then,  as  when  we  are  looking  at  a level  range  of  high 
mountains,  we  can  recognize  the  curve  so  distinctly  that 
a painter,  wholly  aside  from  the  reasons  already  given, 
owing  merely  to  its  unmistakable  appearance,  would  re- 
produce it  in  his  picture.  But  if  so,  why  should  it  not  be 
correspondingly  reproduced — not  wholly,  but  according 
to  the  laws  of  perspective — in  the  supposed  horizontal 
part  of  a wide  building,  standing  above  but  comparatively 
near  us,  and  immediately  in  front  of  the  curved  horizon  ? 
It  may  be  supposed  that,  if  such  a curve  were  introduced, 
this  part  of  the  building  would  not  appear  horizontal. 
But  this  is  a mistake.  It  is  the  only  thing  that  can  make 
it  appear  so.  If  the  curve  be  not  introduced,  that  which 
should  appear  horizontal,  will  appear,  at  the  point  which 
is  nearest  us,  to  sag  downward.  See  Fig.  103,  page  236, 
also — to  be  explained  farther  on — Fig.  108,  page  247. 

There  is  another  principle,  too,  involved  here.  It  is 


240 


PROPORTION  AND  HARMONY. 


this, — that  the  horizontal  line  at  the  exact  height  at 
which  the  eyes,  when  turned  upward,  are  directed, 
represents  to  them,  for  the  time  being,  the  absolute 
horizontal  level,  and  all  other  straight  horizontal  lines 
supposed  to  be  parallel  to  the  first,  will,  at  a point 
perpendicular  to  that  at  which  the  eye  is  directed,  ap- 
pear to  curve  down- 
ward from  the  line  if 
they  are  below  this 
horizontal  level,  or  to 
curve  upward  if  above 
it.  Notice  the  lines, 
all  of  them  perfectly 
straight,  in  the  upper 
triangle  in  Fig.  104, 
this  page.  When  the 
eyes  are  directed  tow- 
ard this  triangle  as  a 
whole,  they  are,  of 
course,  directed  tow- 
ard its  mathematical 
centre;  and  the  lower 
base  line,  of  course,  is  below  this  centre.  Observe,  as 
a result,  how  this  line  appears  to  sag,  or  curve  down- 
ward, at  its  middle  point.  Now  observe  also  the  second 
drawing  in  Fig.  104.  In  this  the  lower  line  of  the  triangle 
is  made  to  curve  slightly  upward  at  its  middle  point.  As 
a result,  this  line  no  longer  appears  to  sag,  but  to  be  per- 
fectly straight.  In  the  lower  drawing  of  this  Fig.  104, 
the  effect  of  an  apparent  curve  in  a really  straight  line  is 
brought  out  still  more  decidedly.  In  this  drawing  two 
similar  triangular  figures  are  placed  together,  but  the 
shorter  sides  of  each  triangle  are  emphasized  by  being 


FIG.  104.— OPTICAL  ILLUSIONS  CAUSED  BY  LINES 
ARRANGED  AS  IN  PEDIMENTS. 

See  pages  240,  241,  242,  250,  254,  256. 


ILLUSIONS  IN  PERSPECTIVE. 


24I 


tripled.  This  emphasis,  according  to  a well-known  mental 
law,  renders  it  impossible  for  the  mind,  when  comparing 
the  two  triangles,  to  confine  attention  to  the  single  line 
forming  the  longer  side  of  the  triangle.  The  central  point 
of  attention,  when  looking  at  each  triangle,  is  drawn  toward 
its  mathematical  centre,  and  the  two  triangles  are  com- 
pared together  as  wholes.  The  effect  produced  by  each 
triangle  therefore  is  the  same  as  that  produced  by  the 
single  triangle  at  the  top  of  this  Fig.  104.  In  both  tri- 
angles, the  long  line  seems  to  curve  away  from  the  angle 
opposite  it,  and  the  two  long  lines, — one  of  the  one  tri- 
angle and  the  other  of  the  other, — though  placed  in  a po- 


S 7^  7^  7^  S'  y/ y/ 

" N W W — 

FIG.  105.  — OPTICAL  ILLUSIONS  WITH  TWO  PARALLEL  HORIZONTAL  LINES. 
See  page  241. 


sition  where  they  are  exactly  parallel,  do  not  seem  to 
be  so. 

When  one  looks  first  at  Fig.  105,  and  observes  that  the 
two  horizontal  lines,  which  are  really  parallel,  seem  at  the 
left  to  move  away  from  each  other,  he  may  suppose  this 
to  be  because  the  ends  of  the  cross  lines  at  that  extremity 
are  farther  apart.  But  he  may  prolong  these  lines,  and 
bring  them  quite  near  together,  without  entirely  chang- 
ing the  illusive  effect.  The  truth  seems  to  be  that,  in 
accordance  with  the  principle  of  perspective  which  draws 
attention  in  the  direction  of  converging  vertical  lines,  as 
may  be  observed  in  the  upper  left  drawing  of  Fig.  102, 
page  235,  the  vertically  directed  lines  crossing  the  upper 
horizontal  line  draw  attention  upward,  and,  because  these 

16 


242 


PROPORTION  AND  HARMONY. 


lines  never  become  perpendicular,  draw  it  also  toward 
the  extreme  right ; whereas  the  vertically  directed  lines, 
crossing  the  lower  horizontal  line,  draw  attention  down- 
ward, and  toward  the  extreme  right.  A single  cross  line 
might  not  have  had  this  effect,  but  the  emphasis  imparted 
by  the  repetition  of  the  lines,  forces  it  upon  the  mind. 
The  result  is  that  both  horizontal  lines— the  one  appear- 
ing to  the  eye  as  it  would  if  the  centre  of  the  field  of 
sight  were  above  the  right,  and  the  other  as  it  would  if 
this  centre  were  below  the  right— are  made  to  seem  to 
bend  away  from  one  another.  That  is  to  say,  what  the 
eye  compares,  is  not  merely  the  two  lines,  but  the  way  in 


106.— OPTICAL  ILLUSIONS  WITH  THREE  PARALLEL  HORIZONTAL  LINES. 
See  pages  242,  243. 


which  each  line  appears  related  to  a central  point,  the 
exact  position  of  which  central  point  is  determined  by 
the  resultant  effects  of  each  horizontal  line  together  with 
the  vertically  directed  lines  crossing  it.  The  effect  is 
evidently  the  same  in  principle  as  that  of  the  apparent 
bending  away  from  each  other  of  the  two  longer  lines  of 
the  two  triangles  in  the  lower  drawing  in  Fig.  104,  page 
240.  The  same  conditions,  differently  presented,  may  ex- 
plain the  apparent  curves  in  the  really  horizontal  lines  in 
Fig.  106,  above.  If  we  place  a series  of  small  upright 
pegs  in  a flat  rubber  band,  and  then  curve  the  band  down- 
ward at  either  side,  all  the  pegs  will  incline  outward  from 
a common  centre.  The  lines  above  the  upper  horizontal 


ILLUSIONS  IN  PERSPECTIVE. 


243 


line  in  Fig.  106  give  us  an  exaggerated  representation 
of  this  arrangement;  and,  on  account  of  the  emphasis 
given  by  their  repetition,  they  force  the  eye  to  consider 
the  horizontal  line  as  related  to  some  imaginary  centre 
below  it,  above  which  centre,  therefore,  the  line  seems  to 
curve  upward.  The  same  is  true  of  the  lower  horizontal 
line  also,  the  lines  crossing  which  have  exactly  the  same 
direction  ; while  the  opposite  is  true  of  the  middle  hori- 
zontal line,  the  lines  crossing  which  are  directed  in  such 
a way  as  to  suggest  a centre  of  attention  above  the  line. 
The  apparent  curving  of  this  line  therefore  is  away  from 
this  centre,  and  accordingly  downward. 

These  illusions  are  explained  somewhat  differently  here 
than  in  Thiersch’s  “ Optische  Tauschungen,”  from  which 
the  drawings  were  borrowed  for  an  article  by  Prof.  Good- 
year in  the  “Architectural  Record.”  Indeed,  in  some  cases 
the  effects  are  owing  to  several  different  causes,  or  to  com- 
binations of  them.  But  the  exact  method  of  explaining 
the  illusions  is  less  important,  for  our  present  purpose,  than 
is  a recognition  of  the  fact  that  they  exist,  and,  in  con- 
nection with  this,  of  the  particular  influence  which  they 
exert  upon  particular  combinations  of  outlines. 

One  not  acquainted  with  the  methods  of  reproducing 
in  color  the  effects  of  nature,  might  suppose  that  it  would 
be  necessary  merely  to  go  into  the  fields,  and  examine 
near  at  hand  the  colors,  appearing,  say,  on  a rose  ora  bush, 
match  them  exactly  with  his  pigments,  and  then  use,  on 
his  canvas,  these  pigments  thus  determined.  But  every 
one  of  experience  knows  that  much  more  is  necessary  ; 
and  this  for  the  simple  reason  that  colors,  when  blended 
and  seen  from  a distance  under  the  influence  of  light  and 
shade,  are  very  different  in  appearance  than  when  seen 
near  at  hand,  A certain  fresco  in  Paris,  when  examined 


244 


PROPORTION  AND  HARMONY. 


closely,  shows  the  flesh  of  a human  figure  to  be  painted 
in  green.  Owing  to  the  influence  of  surrounding  colors, 
no  other  color,  at  a distance,  could  be  made  to  have  the 
effect  of  flesh.  Contours  are  impressed  upon  the  retina 
in  connection  with  the  same  processes  as  those  that  im- 
press colors  upon  it.  These  latter  indeed  frequently 
seem  to  compose  the  whole  image,  outlines  being  merely 
effects  produced  where  one  color  changes  to  another. 
Why  should  it  not  be  recognized  that  to  imitate  the  ap- 
pearance of  outlines  necessitates  the  reproduction  of 
general  effects,  in  the  same  sense  that  it  does  to  imitate 
colors  ? But  is  this  recognized  ? Undoubtedly — in  paint- 
ing and  sculpture  ; but  not,  in  our  times,  in  architecture. 
Yet  it  is  as  rational  for  a man  to  suppose  that  he  can  pro- 
duce satisfactory  effects  of  outline  through  causing  a 
building  to  measure  just  as  many  inches  across  the  top  as 
across  the  bottom,  or  through  causing  a cornice  to  be  ex- 
actly straight,  or  causing  columns  to  be  exactly  the  same 
distance  apart,  as  it  would  be  for  him  to  suppose  that  he 
could  produce  satisfactory  effects  of  color  by  exactly 
matching  with  his  pigments  the  apparent  hues  of  a rose 
or  a bush,  when  examined  close  at  hand. 

The  failure  in  our  times  to  recognize  this  fact  is  all 
the  more  remarkable  in  view  of  the  undoubted  recognition 
of  it,  as  will  presently  be  shown,  not  only  by  the  Greeks, 
but  also  by  the  Egyptians  before  them  and  by  the  Romans 
after  them.  Subsequently,  the  fact  seems  to  have  been 
completely  ignored,  and  though,  within  the  last  half  cen- 
tury, attention  has  again  been  directed  to  it,  its  full  im- 
port has  not  yet  been  apprehended.  Measurements 
designed  to  cause  a building  to  appear  in  perspective  as  it 
does  appear,  i.  e.,  with  outlines  or  spaces  wide,  high, 
straight,  parallel,  or  of  even  sizes,  are  still  confounded 


to 

a 

P* 


246 


PROPORTION  AND  HARMONY. 


with  measurements  designed  to  cause  the  parts  of  the 
building,  when  appearing  as  they  do,  to  seem  to  be  in 
proportion. 

To  avoid  the  confusion  of  thought  resulting  from  con- 
founding these  two  different  aims  it  seems  necessary,  as 
intimated  on  page  180,  to  notice,  first  of  all,  that,  whether 
with  or  without  reference  to  what  we  now  term  proportion, 
there  was  a time  in  history  when  a building  was  looked  upon 
as  presenting  an  appearance  which,  as  in  the  case  of  every 
other  work  of  art,  was  to  be  judged  by  its  general  effect. 
This  is  produced  upon  a spectator  when  examining  it,  as 
one  does  a painting  or  a statue,  from  a certain  definite  eye- 
point,  as  it  is  technically  called,  where  one  can  see  the 
interrelations  of  all  its  members  and  form  an  estimate  of 
the  composition  as  a whole.  In  other  words,  these  build- 
ings were  erected  with  primary  reference  to  the  appear- 
ances that  they  would  present  when  seen  from  a certain 
definite  distant  position. 

The  proofs  of  this  fact  are  abundant.  In  1832,  Mr. 
John  Pennethorne,  an  English  architect,  accidentally,  as  it 
were,  noticed  that  the  architraves  surmounting  the  four 
square  sides  of  the  second  court  of  the  Egyptian  temple 
of  Medinet  Habou  at  Thebes  were  so  constructed  as  to 
lean  forward  at  a middle  point  between  their  ends,  thus 
causing  their  apparently  straight  lines  as  they  passed 
from  corner  to  corner  to  describe  a slight  curve,  or 
entasis  as  it  is  technically  termed.  Notice  the  effect,  ex- 
actly corresponding  to  this,  in  the  line  at  the  side  of  the 
roof  of  the  Maison  Carree,  as  represented  in  Fig.  107, 
page  245,  and  Fig.  108,  page  247.  Returning  to  England, 
he  reread  the  passages  from  the  Latin  writer  Vitruvius, 
partly  quoted  on  pages  256  and  258,  passages  which, 
strange  to  say,  had  been  familiar  to  scholars  for  years,  with- 


FIG.  108.— PHOTOGRAPHIC  EFFECT  OF  CORNICE  CURVE  IN  THE  MAISON 
CARREE. 

See  pages  239,  246,  249,  250,  251,  255,  258. 


?47 


248 


PROPORTION  AND  HARMONY. 


out  suggesting  the  feasibility  of  making  any  attempt  to 
verify  their  statements.  Determining  to  do  this  him- 
self, he  went  to  Athens  in  1837,  made  measurements,  and 
discovered  the  existence  of  certain  curves  in  the  buildings 
there.  About  the  same  time,  two  Germans  also,  Hofer  and 
Schaubert,  did  the  same,  and  published  an  account  of  their 
discoveries  in  the  “ Wiener  Bauzeitung.”  These  discov- 
eries, however,  did  little  more  than  prove  that  the  curves 
existed.  Not  till  the  publication  of  the  “ Principles  of 
Athenian  Architecture,”  detailing  the  results  of  the  more 
searching  and  minute  measurements  of  the  English  archi- 
tect, F.  C.  Penrose,  was  it  made  plain  that  the  curves 
were  not  accidental  but,  probably,  every  one  of  them 
intentional.  Indeed,  they  were  found  to  characterize 
almost  all  the  apparently  straight  lines.  In  connection 
with  this  fact  he  discovered,  too,  many  unexpected  and 
evidently  intentional  variations  of  measurement  of  other 
kinds. 

With  reference  to  the  latter,  as  Prof.  Wm.  Henry  Good- 
year says  in  an  article  on  “ The  Greek  Horizontal  Curves,” 
in  “The  Architectural  Record  ” for  the  quarter  ending  June 
30,  1895,  “ although  we  can  occasionally  trace  some  scheme 
in  the  variations  by  comparing  two  halves  of  one  end  or 
one  side  of  the  building,  instances  of  two  adjacent  meas- 
urements being  equal  are  almost  absolutely  unknown.” 
As  compared  each  with  each,  the  sizes  of  columns,  of  their 
capitals,  of  the  spaces  between  them,  and  of  the  various 
ornaments  in  the  entablatures  over  them  are  seldom  the 
same.  Nevertheless,  notwithstanding  these  curves  and 
irregularities,  Stuart  and  Revett,  who  had  measured  the 
whole  Parthenon  in  1756,  and  Lord  Elgin  and  Cockerell 
and  Donaldson,  who  had  subsequently  tried  to  make  a 
most  careful  study  of  it,  had  failed  to  notice  anything  be- 


ILLUSIONS  IN  GREEK  ARCHITECTURE. 


249 


yond  the  swelling  and  leaning  of  the  columns.  Penrose 
tells  us  that  he  was  months  in  Athens  before  he  could  de- 
tect with  his  eye  even  which  way  a given  column  was  lean- 
ing; and  with  all  his  investigations  in  which  he  did  not 
depend  upon  his  eyes,  he  still  left  many  very  important  facts 
undiscovered.  Prof.  Goodyear,  in  the  article  just  men- 
tioned, gives  an  account  of  his  own  measurements  of  the 
Maison  Carr6e  in  Nimes  and  of  the  Egyptian  temples  at 
Karnak,  Luxor,  and  Edfou,  and  he  says  that  in  all  of 
these  he  has  found  an  outward  curve  of  the  entablature,  as 
represented  in  Fig.  107,  page  245,  and  Fig.  108,  page  247. 
Yet  these  buildings  had  been  inspected  for  years  by 
tourists  and  artists,  intent  on  making  every  discovery 
possible  with  reference  to  their  modes  of  construction. 
Could  anything  afford  more  convincing  proof  that  these 
curves  and  other  irregularities  were  designed  to  produce 
just  what  they  do  produce — i.  e.,  effects  of  regularity — in 
conjunction,  at  times,  as  intimated  on  page  260,  with  those 
of  augmented  width,  height,  dignity,  or  symmetry? 

One  special  contribution  of  Prof.  Goodyear  to  the  gen- 
eral subject  lies  in  his  discovery  that  the  same  form  of 
curve  previously  noticed  by  Mr.  Pennethorne  in  the 
temple  of  Medinet  Habou  is  found  not  only  in  the  Egyp- 
tian temples  at  Karnak,  Luxor,  and  Edfou,  but  also  in  the 
temple  at  Nimes.  As  the  curve  thus  applied  is  not  found 
in  any  of  the  temples  at  Athens;  and  as  Nimes  was 
founded  by  Alexandrine  Greeks  from  Egypt,  this  fact,  in 
his  opinion,  points  to  a direct  Egyptian  influence. 

As  related  to  our  present  line  of  thought,  it  will  be 
recognized  that  the  supposition  that  all  these  buildings 
were  constructed  with  primary  reference  to  producing 
a certain  apparent  effect  when  viewed  from  some  point  or 
points  at  a distance,  is  the  only  one  that  can  furnish  the 


250 


PROPORTION  AND  HARMONY. 


same  reason,  and  a sufficient  one,  for  all  the  different 
methods  of  producing  these  effects, — methods  as  different, 
for  instance,  as  that  in  the  forward  curve  of  the  entab- 
lature represented  in  Fig.  107,  page  245,  and  Fig.  108, 
page  247,  and  as  in  the  upward  curve  of  the  entablature 
represented  in  Fig.  103,  page  236,  or  of  the  stylobate  as  in 
Fig.  109,  page  251.  Moreover,  such  a supposition  is  the 
only  one  that  can  give  the  same  reason,  and  a sufficient 
one,  for  the  application  of  the  same  method  in  order  to 
produce  the  same  effects,  yet  with  almost  infinite  differ- 
ences in  measurements,  in  different  temples.  Here  are 
some  of  these  measurements  as  reported  by  Penrose. 


Buildings. 

Actual  length  of 
the  front  or 
flank  measured. 

Actual  rise  above  a 
straight  line 
joining 

the  extremities. 

Proportional  rise 
corresponding  to  a 
length  of  100  feet. 

Jupiter  Olympus,  stylo- 

bate,  flank  .... 

354-2 

.25  nearly 

.07 

Theseum,  stylobate, 

front 

45- 

.063 

.140 

flank 

102.2 

. IOI 

.097 

Parthenon,  sub-base- 

ment,  front 

104.2 

.150 

.145 

flank 

221. 

•233 

.105 

stylobate,  front  . . 

101.3 

.228 

.225=1.145 » bf 

flank 

228.1 

.355 

.156  = 1.105  ) > a 

entablature  from  east 

front 

100.2 

.171  =f  .228 

.171 

do.  on  flank  restored . 

227. 

.307 

•135 

Propylsea,  entablature.. 

from  east  portico  . . 

68.1 

.119 

-175 

As  will  be  noticed,  all  of  the  measurements  differ,  and 
in  all  regards.  The  same  is  true,  too,  of  the  comparative 
measurements  of  other  parts  of  the  same  and  of  other 
temples.  This  fact  has  caused  no  end  of  perplexity.  It 
has  done  so  mainly,  however,  because,  as  said  on  pages 


IRREGULARITY  IN  GREEK  MEASUREMENTS.  25  I 


29,  and  30,  the  measurements  have  been  thought  to  rep- 
resent certain  mathematical  ratios  supposed  to  be  essen- 
tial to  results  of  proportion.  But,  as  has  been  also  said, 
they  probably  have  nothing  to  do  with  proportion, per  se, 
but  merely  with  producing  the  appearances  to  which, 
after  being  made  to  appear  as  they  do,  the  principles  of 
proportion  apply.  The  best  clue  to  the  interpretation  of 
these  irregulari- 
ties seems  to  be 
afforded  by  the 
methods  of  intro- 
ducing perspec- 
tive into  painting. 

(See  the  quota- 
tion from  Vitruvi- 
us on  page  252.) 

It  is  not  consid- 
ered necessary  in 
this  latter  art  to 
apply  the  laws  of 
perspective  with 
mathematical  ex- 
actness. Each 

draftsman,  in  arranging  his  outlines,  feels  at  liberty  to  stand 
off  from  his  drawing,  and,  as  a result  of  repeated  examina- 
tions and  experiments,  to  use  his  own  ingenuity.  Indeed, 
even  if  these  laws  were  applied  with  mathematical  exactness, 
the  required  measurements  would  differ  with  every  foot  by 
which  a man  stood  nearer  to  his  product,  or  farther  from 
it.  Precisely  so  in  architecture.  A single  glance  at  Figs. 
103,  page  236,  107,  page  245,  or  108,  page  247,  will  show 
that,  in  order  to  produce  any  given  general  effect,  every 
measurement  in  a building  would  have  to  be  changed  with 


FIG.  109.— PHOTOGRAPHIC  EFFECT  OF  CURVED  STYLO- 
BATE AND  COLUMN  OF  THE  PARTHENON. 

See  pages  250,  255,  258,  260. 


252 


PROPORTION  AND  HARMONY. 


every  change  in  the  point  of  view.  Let  the  man  in  Fig. 
107,  page  245,  step  a few  feet  farther  away  from  the  build- 
ing, and  in  order  to  preserve  the  same  effect,  not  only 
would  the  curve  in  the  cornice  have  to  be  lessened,  but 
the  columns  at  either  end  of  the  colonnade  would  have  to 
be  brought  nearer  together.  Let  a temple  placed  upon 
the  brow  of  a hill  be  intended  to  produce  a certain 
effect  upon  those  ascending  it,  and  its  pediment  would 
have  to  be  higher  than  if  it  were  intended  to  produce  the 
same  effect  upon  those  on  a level  with  it  ; or,  as  Vitruvius 
says,  very  unequivocally,  in  book  iii.,  chapter  iii.,  “ To  pre- 
serve a sensible  proportion  of  parts,  if  in  high  situations 
or  of  colossal  dimensions,  we  must  modify  them  accord- 
ingly, so  that  they  may  appear  of  the  size  intended.” 
No  wonder,  therefore,  that  the  Parthenon  which  crowned 
the  Acropolis  (Fig.  95,  page  186),  was  given  a relatively 
higher  pediment  than  the  Theseum  (Fig.  10,  page  36) 
which  stood  on  a level  with  the  plain  surrounding  it. 

In  addition  to  these  facts,  suggested  by  the  methods  of 
applying  the  laws  of  perspective  in  painting,  let  us  recall 
now  that,  in  a sense  not  true  of  our  own  architects,  those 
of  ancient  times  pursued  in  other  regards  the  same 
methods  as  did  their  fellow-artists  in  the  other  arts.  The 
Parthenon  was  not  sketched  in  its  completed  form  upon 
paper,  and  then  let  out  to  some  contractor  to  be  erected 
in  so  many  months.  It  took,  as  some  say,  ten  years,  and, 
as  others  say,  sixteen  years  to  complete  it ; and  most  of 
the  marble  in  it — each  column,  for  instance,  with  its  capital 
— is  said  to  have  been  shaped  after  being  lifted  to  its 
place.  We  know  that  some  of  the  Gothic  cathedrals  were 
almost  entirely  pulled  down  and  rebuilt,  because  their  ap- 
pearance was  not  satisfactory.  Why  should  it  not  have 
been  the  same  with  the  Greek  temples?  In  the  age  in 


ANCIENT  AND  MODERN  METHODS. 


253 


which  they  were  constructed  other  artists  believed — why 
should  not  the  architect  ? — that  a man  should  study  upon 
a product,  if  he  intended  to  have  it  remain  a model  for 
all  the  future.  It  is  natural  to  suppose  that  the  structural 
arrangements  intended  to  counteract  optical  defects,  or  to 
produce  optical  illusions,  were  largely  the  results  of  the 
individual  experiments  of  individual  builders.  If  they 
were  not  so,  why  were  they  invariably  different  in  differ- 
ent buildings?  But  if  they  were  so,  and  if,  therefore,  it 
be  justifiable  to  compare  the  methods  of  arranging  the 
outlines  of  these  buildings  to  the  methods  of  arranging 
outlines  according  to  the  laws  of  perspective  in  painting, 
then  why  is  not  the  general  principle  which  these  ancient 
architects  endeavored  to  fulfil  of  more  practical  impor- 
tance than  any  particular  manner  in  which,  in  any  particu- 
lar case,  they  fulfilled  it  ? More  than  this,  why  might  not 
the  architects  of  our  own  time,  by  applying,  each  for  him- 
self, as  a result  of  his  individual  experiments,  the  same 
general  principle,  produce  approximately  successful  re- 
sults? But  these  they  certainly  cannot  produce  (for  rea- 
sons stated  on  page  26)  until  they  get  out  of  their  heads 
the  conception  that  the  measurements  in  the  ancient 
buildings  are  merely  representative — in  some  mysterious 
way  not  possible  to  fathom — of  ratios  related  to  one  an- 
other as  are  those  of  pitch  in  music.  As  applied  to  this 
case,  at  least,  we  have  an  illustration  of  how  utterly  de- 
structive of  true  practice  in  art  is  a false  theory. 


CHAPTER  XV. 


HARMONY  OF  OUTLINES  : PERSPECTIVE  AS  DETERMINING 
ENTASIS  AND  IRREGULARITY  IN  GREEK  ARCHITECTURE. 

Upward  Curves  in  apparently  Horizontal  Architectural  Lines  Ascribed  to 
Effects  of  Pediment — To  the  Formation  of  the  Eye — An  Explanation  of 
Vitruvius — Ascribed  to  a Desire  to  Increase  Apparent  Size — To  a Desire 
to  Represent  Relationship  to  other  Lines — Forward  Leaning  of  appar- 
ently Perpendicular  Lines — Inward  Leaning  and  Tapering  of  the  Col- 
umns— Designed  Physically  to  Meet  Requirements  of  the  Eye  and 
Artistically  to  Suggest  Height— The  Same  is  True  of  the  Outward  and 
Inward  Curving  of  the  Column’s  Sides — Laws  of  Vitruvius  with  Refer- 
ence to  Columns — Differences  in  the  Measurements  of  Different  Greek 
Columns — Difference  between  the  Greek  and  Roman  use  of  Principles 
— Columns  and  Spaces  at  the  Corners  of  Colonnades — Sizes  of  Columns 
as  Determined  by  their  Positions  in  Exteriors  and  Interiors — General 
Conclusion. 

r"P  HE  references  made  in  the  last  few  pages  to  the  curves 
and  irregularities  discovered  in  the  Greek  temples 
naturally  suggest  an  examination  of  some  of  these  in  detail, 
as  well  as  of  some  of  the  reasons  that  have  been,  or  that 
may  be,  assigned  for  them.  Penrose  tells  us  in  his  “ Princi- 
ples of  Athenian  Architecture,”  chapter  15,  page  104, 
that  the  upward  curve  in  the  entablature  was  “to  obviate 
a disagreeable  effect  produced  by  the  contrast  of  the  hori- 
zontal with  the  inclined  lines  of  a flat  pediment,  causing 
the  former  to  be  deflected  from  the  angles.”  This,  as 
will  be  noticed,  is  exactly  the  effect,  rather  illusive  than 
“ disagreeable,”  produced  by  the  straight  lines  in  the  up- 
per drawing  in  Fig.  104,  page  240,  for  which  effect  a reason 

254 


EN TA SIS  IN  GREEK  ARCHITECTURE. 


255 


is  given  on  page  240,  and  which  effect  is  corrected  in  the 
middle  drawing  of  the  same  figure  by  means  of  a slight 
upward  curve  in  the  lower  horizontal  line.  We  may  there- 
fore conclude  that  Penrose  was  right  in  assigning  this  as 
the  cause  of  the  slight  upward  curve  in  the  entablature 
when  under  a pediment.  At  the  same  time,  the  reason 
given  by  him  may  not  have  been  the  sole  one.  His  own 
words  seem  to  show  that  it  was  not.  His  argument  is  that 
the  curved  entablature  is  not  found  on  the  sides,  but  only 
in  the  fronts — where  alone  the  pediment  is  visible — of 
certain  temples,  noticeably  those  at  Paestum  and  Corinth, 
and  of  the  Propylaea.  But  this  argument  would  have  had 
more  force,  had  not  he  himself — subsequently,  probably — 
discovered  (see  page  250)  many  other  temples  in  which  the 
entablature  at  the  side  is  curved.  Indeed,  Prof.  Goodyear, 
in  the  article  already  quoted  on  page  248,  says  that,  accord- 
ing to  Jacob  Buckhart,  the  very  temple  at  Paestum  men- 
tioned by  Penrose,  has  a side  entablature  leaning  forward, 
like  the  one  in  Figs.  107,  page  245,  and  108,  page  247. 
Moreover,  though  what  Penrose  says  may  explain  the  up- 
ward curve  in  the  entablature  it  would  not  explain  the 
curve  in  the  stylobate,  i.  e.,  the  lower  platform  just  under 
the  columns.  (See  Fig.  109,  page  251.) 

The  truth  seems  to  be  that  the  reason  given  by  Penrose, 
though  correct  so  far  as  it  goes,  is  not  the  only  reason,  nor 
does  it  get  down  to  all  the  principles  underlying  the  sub- 
ject. As  shown  on  page  234,  when  explaining  Fig.  103, 
page  236,  if,  from  a little  distance,  we  look  at  a hori- 
zontal line  before  us,  and  extending  to  both  sides  of  us, 
in  the  degree  in  which  this  line  is  long  its  central  point  in 
front  of  us  will  seem  to  curve  away  from  us,  the  inclina- 
tion of  the  curve  being  upward,  in  case  our  eyes  be  di- 
rected to  what  is  below  the  line,  and  downward,  in  case 


256 


PROPORTION  AND  HARMONY. 


they  be  directed  to  what  is  above  it.  As  shown,  too,  on 
page  240,  when  explaining  Fig.  104,  the  eyes,  when  look- 
ing at  a triangular  pediment,  are  directed  toward  its 
mathematical  centre.  This  is  above  the  entablature,  the 
horizontal  level  of  which,  being  below,  might  seem  to  sag 
downward  unless,  like  the  lower  line  in  the  second  drawing 
in  Fig.  104,  it  really  curved  upward.  So  again,  when 
looking  at  a temple,  the  eyes  are  instinctively  directed 
toward  some  level  above  the  stylobate,  and  its  horizontal 
too  might  seem  to  sag  downward,  if  it  did  not  curve 
slightly  upward.  It  is  said  that  this  appearance  of  sag- 
ging downward  is  very  marked  in  the  celebrated  Walhalla, 
near  Regensburg,  Bavaria,  erected  by  Von  Klenze  under 
the  auspices  of  Ludwig  I.,  in  imitation  of  the  Parthenon, 
but  at  a date  previous  to  that  at  which  in  modern  times 
the  existence  of  these  curves  had  become  known. 

Now  if,  with  these  plain  deductions  from  common- 
sense,  we  turn  to  book  ii. , chapter  iii.,  of  the  “ De  Architec- 
tura  ” of  the  Roman  writer  Vitruvius,  we  shall  find  that 
this  conception  of  what  ought  to  be  done  accords  exactly 
with  his  statement  of  what  was  done  by  the  ancient  build- 
ers. The  stylobate,  or  lower  platform,  he  says  “ ought 
not  to  be  constructed  upon  the  horizontal  level,  but 
should  rise  gradually  from  the  ends  towards  the  centre 
so  as  to  have  there  a small  addition.  ...  If  the  line 
of  the  stylobate  were  perfectly  horizontal,  it  would  appear 
like  the  bed  of  a channel.” 

But  before  we  leave  the  consideration  of  these  horizon- 
tal lines,  another  thing  needs  to  be  said.  If  a long  line 
seem  to  curve  upward  naturally  at  the  centre,  a line  not 
so  long,  by  being  made  to  curve  upward  artificially,  may 
be  made,  for  this  reason,  to  seem  to  be  long.  Therefore,  if 
one  wish  to  increase  the  apparent  length  or  width  of 


PERSPECTIVE  IN  GREEK  TEMPLES. 


257 


a building,  especially  if  it  stand  a little  above  the  specta- 
tor, as  did  the  Parthenon  on  the  Acropolis  at  Athens  (see 
Fig.  95,  page  186),  he  can  accomplish  his  object  by  caus- 
ing the  horizontal  lines  to  curve  upward  slightly  more 
than  lines  of  the  same  length  would  naturally  seem 
to  curve.  We  may  conclude,  therefore,  that  while  one 
object  of  the  Greeks  in  using  these  horizontal  curves  was 
to  meet  the  natural  requirements  of  the  eye,  and  produce 
the  effects  of  nature,  another  object  was,  in  accord- 
ance with  the  requirements  of  art  as  well  as  of  the  eye,  to 
enhance  and  emphasize  the  effects  of  nature.  (See  page 
258.) 

Any  outlines  that  are  used  in  any  way  have  to  be  con- 
sidered not  only  in  themselves,  but  in  their  relations  to 
other  lines.  As  we  shall  find  presently,  the  perpendicular 
side  lines  of  the  columns  of  these  temples  approached  one 
another  as  they  extended  upward.  This  being  so,  to  one 
for  whom  the  centre  of  the  field  of  view  would,  according 
to  what  was  said  on  page  241,  be  drawn  toward  the  pedi- 
ment, the  downward  lines  formed  by  the  outer  edges  of,  at 
least,  the  side  columns  would  be  liable  to  have  the  effects 
of  immense  spokes  in  a wheel,  of  which  the  horizontal 
lines  of  the  platform  beneath  would  seem  to  form  a cir- 
cumference, while  the  slightly  shorter  horizontal  lines  of 
the  entablature  would  seem  to  form  a slightly  shorter  curve 
corresponding  to  this  circumference.  Not  to  make  too 
much  of  this  suggestion,  might  it  not  have  been  partly  to 
correct  this  optical  illusion,  that,  in  both  platform  and 
entablature,  the  centres  of  the  long  horizontal  lines  were 
made  to  curve  upward?  (See  Fig.  103,  page  236.)  And 
might  it  not  have  been  partly  to  correct  the  same  illusion, 
as  well  as  to  fulfil  the  requirements  in  the  case  of  very  high 
horizontal  lines,  as  explained  on  page  236,  that  the  degree 

•7 


258 


PROPORTION  AND  HARMONY. 


of  curvature  was  greatest  where,  as  in  the  Parthenon,  the 
columns  were  relatively  longest  ? 

Before  we  leave  this  subject  of  the  horizontal  lines,  it 
will  be  interesting,  in  view  of  the  discoveries  of  the  for- 
ward inclinations  of  the  entablature  represented  in  Fig. 
107,  page  245,  and  Fig.  108,  page  247,  to  note  a cor- 
responding arrangement  mentioned  by  Vitruvius,  book  ii., 
chapter  iii.  “ All  the  members,”  he  says,  “ placed  above 
the  capital  of  the  columns,  as  the  architrave,  frieze,  cornice, 
tympanum,  etc.,  ought  to  be  inclined  forward  each  the 
twelfth  part  of  its  height  ; since,  if  a person  looking  at  the 
face  of  an  edifice  conceives  that  two  lines  separate  from 
the  eye,  one  of  which  touches  the  bottom,  the  other 
the  top,  of  the  object  of  vision,  it  is  certain  that  that 
which  touches  the  top  is  longer  ; and  the  farther  up  one 
line  extends,  the  more  it  makes  the  upper  part  appear  to 
tip  backward  ; so  that  if  the  members  which  form  the 
face  of  the  upper  portion  are  made  to  lean  forward  the 
whole  appears  to  be  perfectly  upright  and  plumb.” 

Now  let  us  turn  to  the  columns.  First  of  all,  it  has  been 
found  that  they  incline  slightly  inward  toward  the  temple’s 
walls.  (Figs.  103,  page  236,  and  109,  page  251.)  Evidently 
this  was  for  the  purpose,  partly,  of  increasing  the  appear- 
ance of  stability  in  the  structure  as  a whole  by  causing  it 
to  seem  to  rest  upon  an  exceptionally  broad  foundation  ; 
and,  partly  (see  page  259),  of  increasing  the  appear- 
ance of  height  by  causing  the  ascending  lines  to  seem 
to  be  brought  nearer  together  than,  according  to  the  laws 
of  perspective,  they  naturally  would  be  at  no  more  than 
their  actual  elevation  (see  Fig.  103,  page  236).  In  con- 
nection with  this  inward  inclination  of  the  columns,  caus- 
ing the  whole  building  (see  the  measurements  of  the 
Parthenon,  on  page  250)  to  be  narrower  at  its  eaves  than  at 


PERSPECTIVE  IN  GREEK  TEMPLES. 


259 


its  base,  each  of  the  columns  also  was  narrower  at  the 
top  than  at  the  base.  To  such  an  extent  was  this  the 
case,  that,  notwithstanding  the  fact  that  they  leaned 
slightly  toward  the  wall  of  the  building,  their  inner  out- 
line would  have  appeared  to  lean  away  from  this  wall, 
had  not  this  appearance  been  obviated  by  making  the 
caps  of  the  antae  or  pilasters  in  these  walls  bend  slightly 
outward. 

It  need  hardly  be  said  that  these  arrangements  must 
have  been  for  the  same  general  purpose  as  the  curves  in  the 
platform  and  entablature.  They  were  designed,  first,  to 
meet  the  natural  requirements  of  the  eye ; and,  second, 
to  do  this  in  such  a way  as  to  give  artistic  emphasis  to 
the  members,  and  to  increase  their  suggestions  of  length, 
height,  parallelism,  regularity,  symmetry,  or  of  other  aes- 
thetic effects.  To  notice  only  the  diminution  of  the  col- 
umn toward  its  capital, — in  nature,  the  trunks  of  trees,  in 
accordance  with  the  principle  explained  on  page  237,  de- 
crease in  diameter  according  to  the  degree  of  their  height. 
Even  if  they  did  not  do  this,  to  one  looking  at  them  from 
below,  their  higher  diameters,  according  to  the  principle 
explained  on  page  234,  would  seem  to  be  decreased.  For 
this  reason  an  ascending  column  as  broad  at  its  top  as 
at  its  base  has  a tendency  to  appear  to  reverse  this  prin- 
ciple ; and,  according  to  the  laws  of  association,  may  seem 
actually  to  be  broadest  at  the  top.  Moreover,  it  may 
appear  to  be  shorter  also  than  its  real  height,  for,  if  it 
were  tall,  one  would  expect  it  to  appear  relatively  dimin- 
ished. Besides  this,  the  capital  of  a column,  if  distinctly 
broader  than  its  base,  may  cause  the  whole  to  look  top- 
heavy.  But  to  have  the  capital  seem  no  broader  than 
the  base,  the  shaft  immediately  below  the  capital  must  be 
narrower. 


26o 


PROPORTION  AND  HARMONY. 


The  Greek  columns  not  only  diminished  in  diameter 
toward  their  tops,  but  each  of  their  sides,  as  they  ascended, 
described  a slight  hyperbolic  curve,  which  began  by  bend- 
ing outward  a little  from  the  base.  (See  Fig.  109,  page 
25  1.)  It  is  noteworthy  that  this  arrangement  corresponds 
exactly  to  the  requirements  of  the  appearances  of  ascend- 
ing vertical  lines  as  brought  out  in  recent  experiments  and 
explained  on  pp.  237,  238.  When  looking  at  a column, 
an  ideal  line  rising  exactly  in  the  middle  of  it  represents, 
of  course,  the  perpendicular  in  front  of  us;  and  the  foun- 
dation on  which  the  column  rests  represents  the  horizon- 
tal level.  On  page  238,  it  was  said  that  vertical  lines  to 
the  right  and  left  of  the  perpendicular  appear  to  incline 
outward  for  a little  distance  above  the  horizontal  level, 
and  then  to  incline  inward  ; and,  on  the  same  page,  it  was 
said  that  such  lines,  like  horizontal  lines,  undoubtedly 
describe  a slight  curve.  Such  being  the  conditions,  the 
shape  given  by  the  Greeks  to  their  columns  both  pre- 
vented their  sides  from  appearing  to  sag  inward  where 
they  should  not  have  done  so,  and,  according  to  the 
principle  already  mentioned  several  times,  augmented 
their  apparent  height.  As  in  the  case  of  the  horizontal 
lines,  too,  there  were  probably  other  reasons  for  these 
arrangements.  If  the  columns  in  the  Greek  temples  had 
begun  from  their  very  bases  to  be  diminished  in  size, 
their  side  lines,  as  compared  with  those  of  one  another, 
or  of  the  perpendicular  walls  of  the  building  or  of  the 
entrances,  to  say  nothing  of  the  lines  of  the  erect  figures 
of  men  standing  on  the  platform,  would,  for  this  reason, 
have  seemed  to  incline  inward  altogether  too  rapidly. 
At  their  bases,  therefore,  they  began  by  inclining  slightly 
outward.  Possibly  too,  as  the  platform  on  which  the 
columns  rested  was  slightly  curved,  it  was  felt  that  they 


PERSPECTIVE  IN  GREEK  TEMPLES.  26 1 

must  be  correspondingly  curved,  if  they  were  to  appear 
to  correspond  exactly  to  it.  But  whatever  may  have  been 
the  reasons  of  which  the  Greeks  were  conscious,  it  is  evi- 
dent that  they  were  all  connected  in  some  way  with  an 
endeavor  to  meet  the  natural  requirements  of  the  eye, 
and,  at  the  same  time,  to  give  artistic  emphasis  to  the 
members,  and  increase  their  suggestions  of  length,  height, 
parallelism,  regularity,  symmetry,  or  of  other  artistic 
effects. 

Vitruvius,  as  usual  with  him,  gives  very  inflexible  rules 
to  regulate  the  dimensions  of  these  columns.  “ The 
diminution  of  the  shaft,”  he  says,  in  book  iii.,  chapter  ii., 
“ in  its  taper  from  the  top  to  the  bottom,  is  to  be  thus 
regulated.  If  the  height  of  the  shaft  be  fifteen  feet,  the 
upper  diameter  should  be  five  sixths  of  the  lower  ; if  the 
shaft  be  from  fifteen  to  twenty  feet  high,  the  upper  should 
be  eleven  thirteenths  of  the  lower  ; if  thirty  feet  high,  the 
proportion  should  be  thirteen  fifteenths  ; if  from  thirty  to 
forty  feet  high,  the  diminution  should  be  one  seventh  ; if 
from  forty  to  fifty,  the  decrease  should  be  one  eighth. 
To  the  eyes  the  diameter  of  the  column  diminishes  as  its 
height  increases;  hence  to  preserve  the  same  apparent 
proportion  of  the  diameters  it  becomes  necessary  to  de- 
crease those  of  the  upper  portion  of  the  shaft.  The  eye 
alone  is  the  judge  of  beauty  ; and  where  a false  impression 
is  made  upon  it  through  the  natural  defects  of  vision,  we 
must  correct  the  apparent  want  of  harmony  in  the  whole 
by  instituting  particular  proportions  in  particular  parts.” 
This  last  remark  conforms  in  principle  to  that  which  un- 
doubtedly was  the  object  sought  by  the  Greeks.  But  the 
same  cannot  be  affirmed  of  what  is  said  in  this  passage  of 
the  particular  methods  through  which  they  sought  to 
attain  this  object. 


262 


PROPORTION  AND  HARMONY. 


In  the  proportions  supposed  to  determine  the  curva- 
ture of  the  Greek  column  the  same  difference  appears  as 
in  those  supposed  to  determine  that  of  the  horizontal 
line.  Here  are  figures  given  by  Penrose  in  “ The  Prin- 
ciples of  Athenian  Architecture,”  chapter  iv.,  page  44. 


Entasis  (or  swell- 
ing) in  terms  of 
length  of  shaft. 

Ditto  in  terms  of 
lower  diameter. 

Ditto  in 
terms  of 
semi-diminution. 

I 

I 

I 

Erechtheum 

— 

1080 

134 

9 

I 

I 

I 

Theseum 

— 

— 

— 

708 

I40 

16 

I 

I 

1 

Parthenon 

— 

— 

552 

no 

12 

I 

1 

I 

Propylaea,  small  order 

— 

— 

— 

500 

100 

II 

I 

1 

I 

ditto,  large  order  . 

— 

— 

400 

80 

9 

Jupiter  Olympus  . . 

I 

1 

I 

382 

56 

4 

One  or  two  other  statements  of  Vitruvius  with  reference 
to  these  columns  may  be  of  interest.  But  while  reading 
them  it  is  important  to  bear  in  mind  that  their  significance 
lies  not  in  the  figures  given  but  in  the  general  principle 
which  they  exemplify.  The  figures  are  Roman,  the  princi- 
ple is  Greek.  Greek  architecture  was  original,  and  ap- 
parently, for  reasons  already  indicated,  what  might  be 
termed  individual  and  independent.  Roman  architecture 
was  imitative,  and,  as  these  quotations  from  Vitruvius 
show,  traditional  and  mechanical.  The  principles  that 
the  Greeks  sought  to  carry  out  in  a spirit  of  freedom,  the 


PERSPECTIVE  IN  GREEK  TEMPLES. 


263 


Romans  sought  to  carry  out  in  servility  to  the  letter; 
and  it  is  as  true  in  art  as  in  religion  that  “ the  letter 
killeth.” 

“At  the  angles,”  or  corners  of  the  temples,  Vitruvius 
tells  us,  in  book  iii.,  chapter  ii.,  “ the  columns  should  have 
their  diameters  enlarged  by  a fiftieth  part,  because,  being 
from  their  situation  more  immediately  contrasted  with  the 
light,  they  appear  smaller  than  the  others.”  Modern 
measurements  have  shown  that  in  the  Greek  temples  these 
corner  columns  are  not  only  larger  than  those  associated 
with  them,  but  that  the  space  between  them  and  the 
column  nearest  them  is  less  than  between  other  columns 
of  the  series  to  which  they  belong.  In  the  Parthenon, 
according  to  Penrose,  the  spaces  next  to  the  corner  col- 
umns are  only  six  feet  and  a fraction,  whereas  between  the 
other  columns  they  are  eight  feet  and  a fraction.  This 
arrangement,  too,  like  that  of  the  larger  size  of  the  side 
corner  columns,  was  undoubtedly  designed  largely  to 
counteract  the  effects  of  the  light.  Behind  the  space  be- 
tween these  outer  columns  there  was  no  masonry,  whereas 
behind  the  space  between  all  the  other  columns  was  the 
solid  wall  of  the  temple;  and,  as  is  well  known,  the  space 
between  two  pillars  appears  less  where  it  is  filled  in  with 
material  of  the  same  composition,  than  where  it  is  not. 

The  Greeks  probably  had,  too,  another  reason  for  the 
same  device.  The  divisions  indicated  in  each  horizontal 
line  in  each  rectangle  in  Fig.  18,  page  44,  are  all  of  ex- 
actly the  same  length.  Yet  it  is  impossible  to  look  at 
them  without  suspecting  that  the  divisions  nearest  the 
ends  of  the  lines  are  the  longest.  This  is  the  same  as  to 
say  that  to  cause  these  end  divisions  to  appear  of  exactly 
the  same  length  as  the  others,  they  should  be  made 
shorter.  The  reason  why  this  is  so  is  owing,  of  course, 


264 


PROPORTION  AND  HARMONY. 


to  the  roundness  of  the  eye.  When  we  look  at  the  mid- 
dle of  a horizontal  line  there  is  actually  more  eye-surface 
covered  by  the  divisions  at  the  sides  than  there  is  by  the 
divisions  seen  directly  in  front,  which  latter  divisions  are 
opposite  that  part  of  the  eye  which  is  most  nearly  flat. 

Once  more,  Vitruvius  tells  us,  in  book  ii.,  chapter  iv, 
that  “ If  the  width  of  a temple  be  more  than  one  half 
its  length,  the  proportion  should  be  apparently  restored 
thus:  Columns  should  be  placed  within  and  opposed  to 
those  between  the  antae.  These  should  be  of  correspond- 
ing height ; but  their  diameters  should  be  less  in  the 
following  proportions:  if  the  columns  in  front  be  eight 
times  their  diameter  in  height,  the  inner  ones  should  be 
nine  diameters;  if  the  exterior  be  nine  or  ten  diameters 
in  height,  the  interior  should  preserve  a proportionate 
augmentation.  The  difference  in  the  bulk  of  the  columns 
will  not  be  apparent  because  they  will  not  be  seen  con- 
trasted with  the  light.  If,  notwithstanding,  they  should 
appear  too  slender,  the  number  of  flutings  should  be  in- 
creased. Thus,  if  the  columns  in  front  have  twenty-four 
flutes  the  inner  ones  may  have  twenty-eight  or  even 
thirty-two  ; so  that  what  is  in  fact  taken  from  the  bulk 
may  be  restored  by  the  additional  number  of  flutings. 
This  optical  deception  arises  from  the  idea  of  greater 
magnitude  which  is  impressed  by  the  transit  of  the  visual 
rays  over  a greater  surface.  For  if  the  peripheries  of  two 
circles  of  equal  diameter,  one  of  which  is  fluted  and  the 
other  not,  be  measured  by  a line  which  is  made  to  be  in 
contact  with  every  point  of  the  peripheries,  the  length  of 
the  line  will  not  be  the  same  in  both  cases  ; because  in 
one  it  has  been  made  to  touch  every  point  in  the  concave 
surfaces  of  the  flutings  in  the  intervals  between  the  fillets. 
Since  this  deception  therefore  may  be  accomplished,  it  is 


PERSPECTIVE  IN  GREEK  TEMPLES. 


265 


allowable  to  make  columns  which  are  in  confined  situa- 
tions and  little  exposed  to  the  light  less  massive  than  the 
others,  because  their  want  of  bulk  may  be  rendered  im- 
perceptible by  augmenting  the  number  of  flutings  as  cir- 
cumstances may  require.” 

But  enough  has  now  been  said  to  verify  the  statement 
that  the  ancient  architects  in  order  to  fulfil  both  visual 
and  aesthetic,  both  physiological  and  psychical,  require- 
ments erected  their  buildings  with  primary  reference  to 
their  general  effects  when  seen  from  some  definite  point 
or  points  at  a distance.  In  connection  with  this  it  has 
been  shown  also  that  these  architects  differed  materially 
with  reference  to  the  particular  methods  through  which 
to  secure  these  effects,  arriving  at  their  conclusions,  prob- 
ably, as  a result  of  many  individual  experiences  and 
experiments. 

Since  the  printing  of  the  first  edition  of  this  book,  Pro- 
fessor W.  H.  Goodyear  has  discovered  that  the  methods 
attributed  in  this  discussion  to  only  the  ancient  Greeks, 
the  Egyptians,  and  the  Romans,  were  used  also  by  the 
early  Gothic  architects.  He  himself  has  measured  eighty- 
five  of  their  churches  in  Italy  which  have  floors  rising 
between  the  front  door  and  the  chancel,  sometimes,  three 
feet,  while,  often,  the  successive  key-stones  of  the  arches 
between  the  nave  and  the  aisles  descend  in  the  same 
direction, — evidently  to  increase  the  effect  of  distance 
according  to  the  laws  of  perspective.  To  what  extent  the 
same  methods  are  exemplified  in  the  Gothic  churches  of 
northern  Europe,  has  not  yet  been  determined. 


CHAPTER  XVI. 


HARMONY  OF  OUTLINE  : BINOCULAR  VISION. 

Curvature — The  Field  of  Vision  for  Both  Eyes  not  the  Same — The  Horopter 
which  Both  Eyes  See — At  Either  Side  of  the  Horopter  Something  Else 
Seen  by  but  One  Eye  : Its  Influence  on  the  Recognition  of  Relief  in 
Form — This  Fact  as  Developed  in  Stereoscopy — Other  Illustrations — 
Perception  of  Relief  at  the  Sides  of  an  Object  through  Unconscious 
though  Constant  Movement  of  the  Eyes — As  a Result  of  no  Move- 
ment— -Seeing  the  Sides  of  an  Object  Important  to  Gaining  a Concep- 
tion of  its  Form — Shape  of  the  Eyes’  Field  of  Sight,  for  Each  Eye  and 
for  Both  Eyes — The  Horizontal  Shape  Seen  with  the  Least  Effort  is 
Rounded  Backward  — The  Perpendicular  Shape  is  Elliptical  — Con- 
vergence of  Axis,  and  a Lack  of  it  as  Applied  to  Near  and  Distant  and 
to  Many  and  Few  Details — Practical  Experiments  Evincing  Ease  of 
Perception  of  All  Outlines  in  an  Elliptical  Shape — To  Perceive  Out- 
lines of  this  Shape,  no  Conscious  Movement  of  the  Eye’s  Lens  is  Neces- 
sary— Therefore  they  Realize  the  Condition  Required  by  Visual  Rest, 
Enjoyment,  Beauty — This  Fact  may  Explain  the  Use  of  the  Ellipse  in 
Art — The  Ellipse  in  General — In  Vases,  Leaves,  Birds,  Animals, 
Fishes — Human  Form — Its  Like  Curves  are  Accommodated  to  the  Least 
Expenditure  of  Visual  Effort — The  General  Method  through  which> 
when  the  Eye’s  Axis  changes,  it  can  Look  from  One  to  Another  Line 
with  the  Least  Visual  Effort. 

'I  'HUS  far  we  have  been  considering  the  connection 
A between  the  principle  of  perspective  and  the  repre- 
sentation of  straight  lines,  or,  if  of  curves,  of  these  so  far 
only  as  they  may  be  necessary  in  the  art-product  in  order 
to  enhance  the  natural  or  artistic  effects  of  straight  lines. 
We  have  now  to  consider  the  representation  of  lines  that 
are  actually  curved  in  nature.  In  doing  this,  we  shall 
come  upon  certain  facts  which,  though  intimately  con- 

266 


BINOCULAR  VISION. 


267 


nected  with  the  requirements  of  both  perspective  and 
proportion,  have  not  hitherto,  so  far  as  the  author  is 
aware,  been  recognized. 

What  is  to  be  said  of  these  curves,  may  best  be  intro- 
duced, perhaps,  by  observing  that  when  we  examine  care- 
fully an  object  or  scene,  we  seem  to  have  a distinct 
perception  of  one  point  of  it,  as  we  may  say  ; and,  in 
connection  with  this,  to  have  a less  distinct  perception  of 
a small  space,  surrounding  this  point,  as  well  as  a decid- 
edly dim  perception  of  a much  larger  space  surrounding 
the  small  space.  This  larger  space,  i.  e.,  the  space  the 
most  dimly  perceived  of  all,  represents  the  whole  field  of 
sight ; and  we  would  better  begin  here  by  noticing  that  it 
is  not  for  both  eyes  absolutely  the  same.  If,  while  con- 
centrating our  gaze  upon  an  object,  we  close  in  succession 
first  one  eye  and  then  the  other,  we  find  that  in  closing 
our  right  eye  we  have  removed  from  the  sphere  of  vision 
something  that  seemed  indistinctly  visible  at  its  right, 
and  in  closing  our  left  eye  we  have  removed  something 
that  seemed  indistinctly  visible  at  its  left.  This  shows — 
to  quote  from  Dr.  M.  Foster’s  “ Text-Book  of  Physi- 
ology,”  sec.  ii.,  on  Binocular  Vision — that  “ when  we  use 
both  eyes  a large  part  of  the  visual  field  of  each  eye  over- 
laps that  of  the  other;  but  that,  nevertheless,  at  the  same 
time,  a certain  part  of  each  visual  field  does  not  so  over- 
lap any  part  of  the  other.  If  the  right  hand  be  held  up 
above  the  right  shoulder  and  brought  a little  forward,  it 
soon  becomes  distinctly  visible  to  the  right  eye;  it  enters 
into  the  field  of  sight  of  the  right  eye.  But  if  the  right 
eye  be  closed,  the  right  hand  kept  in  this  former  position 
is  not  visible  to  the  left  eye  ; it  is  outside  the  field  of 
sight  of  that  eye;  it  has  to  be  brought  much  further  for- 
ward before  it  comes  into  the  field  of  sight  of  the  left 


268 


PROPORTION  AND  HARMONY. 


eye.”  While  this  is  true,  however, — while  the  field  of 
sight  is  not  for  both  eyes  absolutely  the  same,  it  has  to  be 
acknowledged  that,  when  we  are  closely  concentrating  at- 
tention upon  any  object  or  scene,  that  which  is  visible  to 
only  one  eye  exerts  but  little  influence.  When,  looking 
intently  forward,  we  bring  a hand  at  one  side  of  us  in 
sight  of  only  one  eye,  though  we  are  conscious  that  some- 
thing is  there  the  vision  conveys  only  a vague  impression 
of  what  this  something  really  is.  We  can  hardly  be  said, 
in  any  full  sense,  to  observe  it. 

Let  us  turn,  therefore,  from  that  which  is  noticed  by 
only  one  eye  to  that  which  is  noticed  by  both  eyes,  be- 
cause it  occupies  the  point  where  the  visual  axes  of  both 
eyes  converge.  (See  A and  B in  Fig.  1 13,  page  272.)  This 
is  the  point  which  is  technically  termed  the  horopter. 
With  reference  to  the  character  or  shape  of  this,  physi- 
cists have  not  yet  come  to  any  agreement.  Joseph  Le 
Conte  tells  us  in  his  work  on  “ Sight  ” that  Aguilonius, 
the  inventor  of  the  term,  believed  it  to  be  a plane; 
Claparbde,  a surface ; Pr6vost  and  Muller,  the  circum- 
ference of  a circle,  and  Helmholtz,  to  be  sometimes  a circle, 
but  to  vary  according  to  the  position  of  the  point  of 
sight.  That  this  horopter  exists,  however,  which  is  all 
that  we  need  to  know  here,  is  universally  admitted. 

But  now  the  question  comes  whether  any  part  of  the 
field  of  sight  between  the  horopter  and  the  exceedingly 
dim  outside  limits  of  this  field  which  were  mentioned  in 
a former  paragraph,  exerts  a distinct  visual  effect  which 
must  be  considered  in  calculating  the  general  influence  of 
outlines.  In  other  words,  is  any  effect,  essential  at  times 
to  that  of  form,  produced  in  the  region  immediately  sur- 
rounding the  horopter,  of  which,  of  course,  we  have  a less 
distinct  perception  than  of  it  ? In  order  to  determine 


BINOCULAR  VISION. 


269 


this,  let  us  begin  by  holding  in  front  of  the  eyes,  the  fore- 
finger of  one  hand,  represented  either  by  a or  by  a'  in 
Fig.  no,  and  then  immediately  in  front  of  this  finger,  the 
forefinger  of  the  other  hand,  represented  either  by  b or  by 
b' . As  we  do  so,  we  shall  find  the  effect  indicated  in  Fig. 
no,  and  if  we  hold  the  fingers  near  enough  to  our  eyes 
and  concentrate  our  gaze  upon  the  farther  finger  of 
the  two,  represented  by  A in  Fig.  hi,  we  shall  see 


I JL 


FIG.  110.— FINGER  BEHIND  AN- 
OTHER AS  SEEN  BY  ONE  EYE. 

By  left  eye  (I) 

By  right  eye  (II) 

See  page  269. 


I a 

FIG.  Ill— FINGER  BEHIND  ANOTHER  AS 
SEEN  WITH  BOTH  EYES. 

When  looking  at  back  finger  (I) 

Or  at  front  finger  (II) 

See  pages  269,  278,  279,  280. 


the  finger  in  front  of  it  dimly  doubled  as  in  b and  b' ; 
and  that,  if  we  concentrate  our  gaze  upon  the  finger 
nearer  to  the  eyes,  represented  by  B in  Fig.  ill,  we  shall 
see  the  farther  finger  dimly  doubled,  as  in  a and  a'.  In 
other  words,  we  shall  find  that,  while  we  are  looking  at 
one  finger  with  both  eyes,  which  finger  therefore  is  at  the 
horopter,  where  the  visual  lines  or  axes  of  both  eyes  cross, 
each  eye  for  itself  sees  the  other  finger  also,  but,  as  this  is 
not  in  the  place  where  the  visual  lines  or  axes  of  both 
eyes  cross,  each  eye  sees  it  in  a different  place.  Notice, 
too,  that  the  farther  from  the  finger  seen  single  we  re- 
move the  apparently  doubled  finger,  the  farther  apart  do 
its  two  dim  representatives  seem  to  be.  Again,  if  we 


270 


PROPORTION  AND  HARMONY. 


stand  a very  thin  book  in  such  a way  as  to  have  its  back 
directly  in  front  of  our  two  eyes  looking  at  it  conjointly, 
and  then,  without  changing  our  position,  close  the  right 
eye  and  look  at  it  with  the  left  eye,  we  shall  distinctly 
see  the  left  side  of  the  cover.  Then  again,  if  we  close 
the  left  eye,  and  look  at  it  with  the  right  eye,  we  shall 
just  as  distinctly  see  the  right  side  of  the  cover.  If  now, 
opening  both  eyes,  we  once  more  look  at  its  back,  we 
shall  not  see  either  side  as  distinctly  as  before ; but  we 
shall  have  a perfectly  clear  impression  of  an  effect  pro- 
duced by  both  sides, — an  effect  enabling  us,  as  it  were,  to 
look  around  the  corners  of  the  back,  and  recognize  its 
form.  Or  if  we  cannot  do  this  in  every  sense,  we  can  ob- 
tain at  least  an  impression  that  the  book  as  a whole 
stands  out  in  relief  from  whatever  is  behind  it.  If  now, 
once  more,  we  look  straight  at  the  back  of  the  book  with 
only  one  eye,  we  shall  perceive  that  such  a view  of  it 
very  much  lessens  this  last  impression — that  of  being 
able  to  look  around  the  corners  and  recognize  the  form 
in  relief. 

This  is  the  fact  with  reference  to  binocular  vision 
which  is  applied,  as  probably  most  of  us  know,  in  stereo- 
scopy. In  preparing  stereoscopic  views,  two  photographs, 
taken  from  different  positions,  a few  feet  apart,  are  made 
of  the  same  object,  or  scene.  Then  they  are  placed  to- 
gether side  by  side  on  a card,  in  front  of  two  glasses 
through  which  they  are  intended  to  be  seen,  the  photo- 
graph taken  at  the  right  being  in  front  of  the  right  eye, 
and  that  taken  at  the  left  being  in  front  of  the  left  eye. 
As  thus  arranged,  each  photograph  is  supposed  to  repre- 
sent the  object  of  view  as  it  is  seen  in  nature  by  one  of 
the  eyes  regarding  it,  but  not  by  the  other  eye.  Any  one 
familiar  with  the  effects  of  the  stereoscope,  knows  how 


BINOCULAR  VISION. 


271 


much  more  natural  and  satisfactory  views  so  doubled  are 
than  are  those  of  a single  photograph.  Especially  is  this 
the  case  with  representations  of  statues,  or  of  any  objects 
the  impressions  conveyed  by  which  depend  upon  the  ap- 
pearance of  thickness  of  form,  particularly  of  that  kind  of 
thickness  which,  for  full  effect,  needs  to  convey  the  im- 
pression of  being  rounded  at  the  sides.  See  Fig.  112, 
page  272,  as  explained  on  the  same  page. 

Not  only  the  stereoscope,  but  other  things  with  which 
all  are  familiar  can  be  explained  only  upon  the  hypothesis 
that  each  eye  has  a different  field  of  view.  If  we  look  at 
a comparatively  large  object,  like  a typewriter,  near  at 
hand,  first  with  a single  eye,  and  then  with  both  eyes,  we 
shall  find  ourselves,  at  a certain  distance,  consciously 
shifting  the  glances,  or,  as  a physicist  would  say,  the  axis 
of  the  single  eye  first  to  one  side  of  the  object,  and  then 
to  the  other,  because  only  thus  can  we  make  out  its  exact 
shape.  But,  at  the  same  distance,  both  eyes  looking  to- 
gether can  perceive  the  shape  without  any  change  or,  at 
least,  any  conscious  change  of  axis. 

This  word  conscious , just  used,  introduces  a question 
which,  as  will  be  recognized  presently,  has  an  important 
bearing  upon  aesthetic  effects  as  related  to  this  particular 
subject.  The  question  is  whether  the  eyes,  when  direct- 
ing attention  away  from  a single  point  in  an  object  to 
the  whole  object,  including  its  two  side  contours,  do  this 
by  a single  act  which  focusses  attention  on  a more  dis- 
tant background  in  front  of  which  the  two  contours  are 
clearly  perceptible ; or  do  so  by  many  successive  acts, 
which  focus  attention  first  on  the  single  point  and  then  on 
one  and  the  other  of  the  contours,  and,  finally,  as  a result 
of  successive  examinations,  draw  a general  inference  with 
reference  to  the  form  as  a whole.  To  determine  how  the 


2J2 


PROPORTION  AND  HARMONY. 


eyes  act  in  these  cases,  two  drawings  represented  in 
Fig.  1 12,  are  given  by  Le  Conte  in  his  “Sight.”  By 
placing  a sheet  of  paper  between  the  two  eyes,  in  such  a 
way  as  to  exclude  a view  of  the  right  drawing  from  the 
left  eye,  and  of  the  left  drawing 
from  the  right  eye,  and  then  looking 
at  the  two  drawings,  at  a certain 
distance  the  two  will  be  found  to 
be  blended  into  one  ; and,  in  this 
one,  we  shall  apparently  be  looking, 
not  at  lines  described  on  a flat  sur- 
face, but  at  what  resembles  a wire 
net  standing  on  end,  the  smaller 
end  of  which,  represented  by  the 
smaller  circles,  seems  nearer  us,  and 
the  larger  end,  represented  by  the 
larger  circles,  seems  farther  from  us. 


FIG.  113.— PARTS  OF  OB- 
JECT, AS  SEEN  WITH 
NEAR  AND  DISTANT 
BACKGROUND. 

py  py  object;  Ay  By  back- 
grounds: L and  Ry  eyes; 
iiy  nose. 

See  pages  234,  268, 
273,  280. 

The  explanation  of  this  effect  is,  that  to  see  both  cir- 
cles equally  well  from  the  same  distance,  the  eyes,  in 
taking  in  all  sides  of  the  larger  circle,  must  adjust  them- 
selves to  a more  remote  background,  for  which  reason 
the  larger  circle  seems  more  remote  from  us  than  the 


FIG.  112.— SAME  OBJECT  SEEN  DIFFERENTLY  BY 
EACH  EYE.  NEAR  AND  DISTANT  BACKGROUND. 

See  pages  271,  272,  274,  280. 


BINOCULAR  VISION. 


273 


smaller  circle.  The  same  effect  is  illustrated  in  a differ- 
ent way  in  Fig.  113,  page  272.  In  this,  a and  a'  repre- 
sent the  two  side  contours  of  the  object  seen  with  the 
eyes  when  adjusted  to  a background  at  A;  and  b and 
b'  represent  the  two  side  contours  of  the  object  seen 
with  the  eyes  when  adjusted  to  a background  at  B.  L 
and  R represent  the  left  and  right  eyes,  n the  nose,  and 
ms  the  paper  placed  between  the  eyes.  Fig.  1 14, 
will  show  what  is  meant  by  the  eyes  being  adjusted 
to  take  in  one  rather  than  another  background,  a in  this 


FIG.  114.— LENS  OF  EYE  ADJUSTED  TO  NEAR  (N)  AND  DIS- 
TANT (F)  OBJECTS. 
ay  aqueous  humor  ; d , ciliary  muscle. 

See  pages  231,  273,  323. 


figure  representing  the  aqueous  humor,  F the  crystalline 
lens  made  flatter,  and  thus  adjusted  to  take  in  a more  dis- 
tant background  ; N the  same  made  more  rounded  in  order 
to  take  in  a nearer  background  ; and  d the  ciliary  muscle 
which  does  the  work.  It  will  be  perceived  that  the  ad- 
justing of  the  eye  to  one  background  or  the  other  requires 
the  exertion  of  considerable  muscular  energy.  The  ques- 
tion before  us  now,  the  aesthetic  bearing  of  which  will  be 
brought  out  presently,  is  with  reference  to  the  degree  or 
quality  of  the  effort  expended  by  the  eyes  in  perceiving 
outlines,  first  at  the  one  and  then  at  the  other  background. 
According  to  Le  Conte,  in  his  “ Sight  ” (Binocular  Vi- 

18 


274 


PROPORTION  AND  HARMONY. 


sion,  chapter  iv.),  the  answer  to  this  question,  as  given 
by  Briicke,  Brewster,  and  Prevost,  is  as  follows : “ In  re- 
garding a solid  object  or  a natural  scene,  or  two  stereo- 
scopic pictures  in  a stereoscope,  the  eyes  are  in  incessant 
unconscious  motion,  and  the  observer,  by  alternating- 
greater  and  less  convergence  of  the  axes,  combines  suc- 
cessively the  different  parts  of  the  two  pictures,  as  seen 
by  the  two  eyes,  and  thus  by  running  the  point  of  sight 
back  and  forth,  reaches  by  trial  a distinct  perception  of 
binocular  perspective  or  binocular  relief.”  This  explana- 
tion supposes  that  the  eye  does  not  take  in  the  whole 
form  at  once,  but  as  a result  of  incessant  action.  Notice, 
nevertheless,  that  it  is  acknowledged  that,  of  this  action, 
the  mind  is  unconscious.  On  page  271  it  was  said  that  in 
trying  to  make  out  the  shape  of  a typewriter  with  one 
eye  we  are  constantly  conscious  of  shifting  attention  from 
one  side  of  the  machine  to  the  other.  It  is  something  to 
have  it  acknowledged  that  when,  with  both  eyes,  we  look 
at  both  front  and  sides  of  an  object,  both  sides  of  which 
can  be  seen  only  as  the  eyes’  lenses  are  adjusted  to  take  in 
a comparatively  distant  background,  we  are  unconscious 
of  this  action. 

But  does  this  action  take  place  ? Wheatstone’s  theory, 
as  stated  by  Le  Conte  (Binocular  Vision,  chapter  iv.),  is 
that  “in  viewing  a solid  object  or  a scene,  two  slightly  dis- 
similar images  are  formed  in  the  two  eyes,  as  already  ex- 
plained ; but  the  mind  completely  unites  or  fuses  them 
into  one.”  Notice  again  what  is  said  on  page  272  of  Fig. 
1 1 2.  Le  Conte  says  also  that  “ the  instantaneous  percep- 
tion of  binocular  relief  is  demonstrated  by  the  now  cele- 
brated experiment  of  Dove.  If  a natural  object  or  a 
scene  or  two  stereoscopic  pictures  be  viewed  by  the  light 
of  an  electric  spark  or  a succession  of  electric  sparks,  the 


BINOCULAR  VISION. 


275 

perspective  is  perfect,  even  though  the  duration  of  such  a 
spark  is  only  ^g-g'o'  a second  of  time.  It  is  inconceiv- 
able that  there  should  be  any  change  of  optic  convergence, 
any  running  of  the  point  of  sight  back  and  forth,  in  the 
space  of  -2xro~o  °f  a second.  Evidently,  therefore,  binoc- 
ular perspective  maybe  perceived  without  such  change  of 
convergence.  This  point  is  certainly  one  of  capital  im- 
portance. The  instantaneous  perception  of  relief  is  fatal 
to  Dr.  Briicke’s  theory  in  its  pure  unmodified  form.” 
Then,  after  mentioning  his  own  experiments  confirming 
Dove’s  discoveries,  Le  Conte  gives  his  own  theory  thus : 
“ All  objects  or  points  of  objects  either  beyond  or  nearer 
than  the  point  of  sight  are  doubled.  ...  In  case  of 
double  images  each  eye,  as  it  were,  ‘ knows  its  own  image,’ 
although  such  knowledge  does  not  emerge  into  distinct 
consciousness.  Thus  I conclude  that  the  mind  perceives 
relief  i?istantly,  but  not  immediately  ; for  it  does  so  by 
means  of  double  images,  as  just  explained.  This  is  all 
that  is  absolutely  necessary  for  the  perception  of  relief ; 
but  it  is  probable — nay,  it  is  certain — that  the  relief  is 
made  clearer  ” — i.  e.,  may  be  made  clearer — “ by  a ranging 
of  the  point  of  sight  back  and  forth,  and  a successive  com- 
bination of  the  different  parts  of  the  object  or  scene  or 
picture  as  maintained  by  Brucke.” 

Now  let  us  apply  the  same  principle  not  to  relief  merely 
but,  in  connection  with  it,  to  the  method  of  perceiving  in 
connection  with  the  front,  the  two  series  of  outlines  de- 
scribing the  two  sides  of  an  object  as  it  stands  fronting 
us  ; and,  in  carrying  out  our  purpose,  let  us  recall  the 
experiment  with  the  book  mentioned  on  page  270.  As  we 
stand  the  book  up  with  its  back  exactly  facing  us,  we  see 
more  of  both  its  side  covers  while  looking  at  it  with  two  eyes 
than  we  do  while  looking  with  one  eye  ; but  we  do  not  see 


2 y6 


PROPORTION  AND  HARMONY. 


as  much  of  either  side  cover  as  we  do  while  looking  at  it 
with  one  eye.  Now  whether  we  explain  the  effect,  when 
using  both  eyes,  by  saying  that  it  results  from  the  inces- 
santly alternating  action  first  of  one  eye,  and  then  of  the 
other  ; or  from  a synchronous  unchanging  action  of  both 
eyes  together,  we  are  obliged  to  infer  that  the  general  ef- 
fect is  not  a combination  of  the  two  different  perceptive 
actions  of  the  eyes.  If  it  were,  we  should  with  both  eyes 
see  both  sides  of  the  cover  as  plainly  as,  with  one  eye,  we 
see  one  side  of  it.  As  we  experience  the  effect,  it  is  a re- 
sultant. A resultant  of  two  forces  never  corresponds  to 
either  the  one,  or  the  other,  or  to  both  in  their  entirety. 
It  represents  each  as  modified  by  the  other. 

Now  we  are  prepared  to  retrace  our  steps  somewhat, 
and  consider  the  bearing  of  what  has  been  said  upon  the 
particular  subject  of  which  this  chapter  was  to  treat, 
namely,  curvature.  Let  us  begin  by  trying  to  determine, 
so  far  as  we  can,  the  exact  shape  of  the  field  of  sight.  As 
applied  to  each  eye  singly,  Dr.  M.  Foster,  in  his  “ Text- 
Book  of  Physiology,”  says  “ The  dimensions  of  the 
field  of  sight  for  one  eye  will,  even  in  the  same  individual, 
vary  with  the  width  of  the  pupil  and  other  dioptric  ar- 
rangements of  the  eye  ; individual  variations  are  also 
considerable  ; but  the  ordinary  dimensions  may  be  stated 
as  subtending  an  angle  of  about  1 45 0 in  the  horizontal  and 
about  100°  in  the  vertical  meridian.  . . . The  outline 

of  the  field  is  an  irregular  one,  and  stretches  farther  toward 
the  temporal  side,”  i.  e.,  the  side  nearest  the  temple.  (See 
Fig.  1 1 5,  page  278.)  And  why  this  should  be  so,  most  of  us 
can  recognize  upon  closing  one  eye,  and  trying  to  look 
forward  with  the  other.  We  shall  usually  detect  the  pres- 
ence of  the  nose,  which,  of  course,  is  the  same  as  to  say 
that  it  limits  the  field  of  vision  of  the  eye  on  that  side 


SHAPE  OF  FIELD  OF  SIGHT. 

on  which  it  appears.  In  the  same  way,  too,  it  is  evident 
that,  in  certain  cases,  the  eyelids  and  lashes  have  an 
influence.  But,  though  the  whole  field  of  vision  may 
have  irregular  outlines,  extending  just  as  the  field  of 
each  eye  does  somewhat  farther  in  a horizontal  than  in 
a vertical  direction,  notice  that  the  pupil  of  the  eye  is 
itself  circular,  and  that  objects  which  can  be  seen  with  ex- 
actly the  same  degree  of  clearness  are  generally  seen  at 
very  nearly  the  same  distance  from  the  pupil’s  centre. 
If,  for  instance,  there  were  an  exactly  similar  nose  exactly 
similarly  situated  on  each  side  of  the  eye,  no  one  doubts 
that,  to  one  looking  straight  forward,  both  noses  would 
produce  an  exactly  similar  impression  of  their  presence. 
The  mere  fact  that  there  happens  to  be  no  nose  on  the 
temple-side  of  the  eye,  while  widening  the  actual  outline 
of  the  field  of  vision  on  this  side,  does  not  change  the 
principle  that  the  same  degree  of  clearness  in  outline  will 
generally  be  found  in  every  direction  at  the  same  distance 
from  the  point  on  which  the  eye’s  centre  is  fixed. 

The  bearing  of  this  upon  the  subject  before  us  is  that 
it  is  approximately  appropriate  to  represent,  not  the 
whole  field  of  vision  but  that  smaller  field  of  compara- 
tively distinct  vision  mentioned  on  page  267,  a field  im- 
mediately surrounding  x and  x in  Fig.  1 15,  page  278,  by  a 
circle.  Nor,  even  if  it  be  insisted  that  this  should  be  a 
circle  elongated  horizontally,  will  anything  that  is  to  be 
said  here  be  found  to  be  inconsistent  with  such  a concep- 
tion of  it.  But  though  the  field  of  distinct  sight  for  one 
of  the  eyes  be  circular,  it  does  not  follow  that  this  is  true 
of  the  field  for  both  eyes  when  looking  together.  If  we 
compare  Fig.  115,  page  278,  with  Fig.  116,  page  278,  we 
shall  perceive  that  this  field  for  both  eyes  is  appropriately 
represented  neither  by  the  single  circle  at  the  left  of  Fig. 


278 


PROPORTION  AND  HARMONY. 


ii 6,  nor  by  the  two  separated  circles  at  the  right  of  this 
figure ; but  rather  by  the  space  enclosed  between  the  two 
circumferences  of  the  circles  where  they  overlap,  as  in  the 
second  and  third  drawings  of  this  figure. 

Of  these  drawings,  notice  now  that  the  first  from 

the  left  represents  the  more 
clearly  of  the  two  the  result 
that  would  follow,  were  we  to 
describe  about  each  x in  Fig. 

1 15  a circle  the  circumference 
of  which  would  pass  exactly 
through  the  other  x.  This  be- 
ing so,  let  us  ask  what  shape  in 
an  object  would  best  enable  the 
eyes  to  see  all  its  outlines  in  a 
single  unchanged  glance  or,  at 
least, — to  recall  what  was  said  on  page  274,— in  a single  un- 
consciously changed  glance,  or  with  the  least  visual  effort. 
In  answering  this  question,  let  us  divide  it,  and  make  it 
apply,  first,  to  a shape  considered  horizontally,  i.  e.,  from 

O GD  00  OO 

FIG.  116.— CIRCLES  ILLUSTRATING  FIELD  OF  DISTINCT  VISION  FOR  BOTH  EYES 

TOGETHER. 

See  pages  277,  280,  288. 


FIG.  1 1 5. — FIELD  OF  VIEW  OF  BOTH 
EYES  AND  OF  EACH  EYE. 

From  Foster’s  “ Anatomy.” 

See  pages  276,  277,  278,  279. 


side  to  side  when  facing  us.  We  may  gain  a clue  to  the 
right  answer  from  Fig.  111,  page  269.  Suppose  that  we 
be  looking  with  both  eyes  at  an  object,  the  middle  front 
of  which  is  in  a place  corresponding  to  that  represented  by 
B in  Fig.  ill  ; and  its  two  sid'es  in  places  corresponding 
to  those  represented  by  a and  a in  the  same  figure.  In 


SHAPE  OF  FIELD  OF  SIGHT. 


279 


this  case,  the  B would  evidently  be  seen  at  the  point  rep- 
resented by  f in  Fig.  1 1 5 : and  the  a and  a at  the  points 
represented  by  x and  x in  Fig.  1 1 5 ; and,  if  so,  the  natural 
effect  produced  by  binocular  vision  as  represented  by  a 
and  a in  Fig.  hi,  would  reinforce  the  effect  produced  by 
the  two  sides  as  seen  at  x and  x in  Fig.  115.  In  fact,  the 
effect  represented  by  a and  a in  Fig.  in,  when  the  fin- 
gers are  placed  as  explained  on  page  269,  is  no  longer  per- 
ceived when,  at  the  same  distance,  we  are  looking  at  the 
front  (B)  of  an  object,  the  sides  of  which  are  in  the  places 
respectively  represented  by  a,  and  a.  Now,  in  addition 
to  what  has  been  said,  it  needs  to  be  observed  here,  if  we 
are  to  complete  the  answer  to  this  part  of  our  question, 
that,  in  order  to  accommodate  itself  to  the  natural  round- 
ing of  the  eye,  the  outline  of  the  object  between  B and  a 
or  a,  as  represented  in  Fig.  in,  or — what  is  the  same — 
between  that  which  is  seen  at  f and  at  x and  x,  as  repre- 
sented in  Fig.  1 15,  would  not  be  a straight  line,  as  if 
there  were  a sharp  angle  at  the  middle  of  the  front,  as  at 
B in  Fig.  in,  or  as  seen  at  f in  Fig.  115  ; but  this  out- 
line would  be  a line  turning  toward  the  backgrounds  at  a 
and  a,  or  as  seen  at  x and  x,  by  regular  degrees.  In 
other  words,  the  shape  would  be  that  produced  by  a 
curved  line,  which  is  the  same  as  to  say  that  the  object 
considered  horizontally,  i.  e .,  from  side  to  side,  would  be 
rounded  from  its  middle  front  backward. 

Now  let  us  take  up  the  second  part  of  our  question, 
and  ask  what  shape  in  an  object  when  considered  perpen- 
dicularly, i.  e.,  from  top  to  bottom,  would  best  enable  the 
eyes  to  see  all  its  outlines  at  a single  unchanged  or,  at 
least,  unconsciously  changed  glance.  Recalling  what  was 
said  on  page  278,  namely,  that  the  field  of  distinct  vision 
for  both  eyes  together  would  be  appropriately  represented 


28o 


PROPORTION  AND  HARMONY. 


by  the  space  enclosed  between  the  intersecting  circles  in 
the  second  and  third  drawings  in  Fig.  1 1 6, — is  it  not  evi- 
dent that  some  shape  fitting  into  this  space  would  best 
fulfil  the  requirement  for  which  we  are  in  search?  The 
space  has  the  shape  termed  by  botanists  ellipticdanceolate, 
— an  ellipse  pointed  ; and  of  all  outlines  wholly  curved, 
those  of  an  upright  ellipse  fit  into  it  most  nearly. 

The  explanation  for  the  formation  of  this  shape  between 
the  two  circles  is,  as  indicated  on  page  278,  that,  at  dis- 
tances farther  off  than  the  object,  or  than  the  part  of  the 
object  at  which  both  eyes  are  looking,  there  are  places 
upon  which  attention  is  not  concentrated,  and  in  these 
places  the  respective  fields  of  distinct  vision  for  the  two 
eyes  cross  in  such  ways  that  each  eye  sees  a different 
circle.  But  it  must  not  be  supposed  that  this  condition 
accompanies  the  perception  of  objects  or  of  parts  of  ob- 
jects at  merely  different  distances,  as  in  the  cases  of  the 
two  fingers  in  Fig.  111.  It  accompanies  the  perception 
of  objects  at  the  same  distance  when  attention  is  more  or 
less  concentrated  upon  a larger  or  a smaller  part  of  them. 
When  we  see  a man,  we  may  concentrate  our  attention 
upon  some  ornament  that  he  wears— -a  buckle  or  a button 
— to  such  an  extent  as  not  to  see  clearly  anything  else. 
Or  we  may  consciously  relax  from  the  effort  at  concen- 
tration, which  means  that,  by  changing  the  form  of  the 
lens,  we  may  re-adjust  the  focus  of  each  eye,  or  let  it  ad- 
just itself,  so  as  to  take  in  a more  distant  background  ; 
and  then,  at  the  same  time,  without  noticing  particularly 
this  background,  we  may  notice  that  which  stands  in  front 
of  it,  and  thus  see  clearly  the  man’s  whole  form.  (See 
Figs.  1 12,  page  272,  and  1 1 3,  page  272.)  Of  course,  when 
this  is  done,  it  is  some  space  like  that  enclosed  by  both 
circles  in  the  second  drawing  in  Fig.  116,  page  278,  that 


SHAPES  PERCEIVED  WITH  LEAST  EFFORT.  28 1 


represents,  at  a point  nearer  than  the  background,  the 
limits  of  the  sphere  of  distinct  vision  for  both  eyes.  To 
apply  this  to  the  illustration  used  on  page  270,  supposing 
the  back  of  a book  to  be  exactly  in  this  enclosed  space, 
the  right  eye,  when  the  left  was  shut,  would  see  its  right 
covers  extending  outside  this  space  toward  the  outer  cir- 
cumference of  the  right  intersecting  circle  ; and  the  left 
eye,  when  the  right  was  shut,  would  see  the  left  cover 
extending  toward  the  outer  circumference  of  the  left 
circle.  But  both  eyes,  when  looking  together,  would  see 
clearly  nothing  outside  the  enclosed  space. 

As  already  intimated,  it  follows  that,  if  what  has  been 
said  be  true,  the  whole  of  a form  facing  us  can  be  recog- 
nized with  ease,  i.  e.,  in  a single  glance,  or,  at  least,  a single 
conscious  glance  (see  page  271),  in  the  degree  in  which  it  is 
conformed  to  vertical  elliptic-lanceolate  outlines.  Indeed, 
this  fact,  thus  theoretically  unfolded,  can  be  confirmed  by 
practical  experiments.  If  we  describe  at  the  nearest  point 
at  which  it  is  possible  to  perceive  all  its  outlines,  an  ellipse 
longer  vertically  than  horizontally,  and  about  it  a circle 
of  the  same  diameter  as  the  vertical  length  of  the  ellipse, 
there  will  be  not  a few  who  will  find  it  slightly  more  easy 
at  a single  glance,  or  without  consciously  changing  the 
axis  of  the  eye,  to  perceive  all  the  outlines  of  the  former 
than  of  the  latter.  If  we  describe  about  the  circle  and 
ellipse  a square  of  the  same  diameter  as  the  circle,  no 
one  can  see  all  its  outlines  without  consciously  changing 
the  axis  of  the  eye,  as  when  glancing  from  corner  to  cor- 
ner; and  if  we  describe  about  the  square  a rectangle  of 
the  same  vertical  but  twice  the  horizontal  dimensions,  we 
cannot  see  all  its  outlines  without  changing  the  axis  still 
more  consciously. 

We  have  found  now  that  the  difference  between  in- 


282 


PROPORTION  AND  HARMONY. 


specting  carefully  some  particular  ornament,  as  a button 
or  a buckle  on  a man’s  form,  and  taking  in  a general  view 
of  his  form  as  a whole,  is  the  difference  between  conscious 
convergence  of  axis  or  concentration  of  sight  and  no  con- 
sciousness of  it.  We  have  found  also  that  the  method 
through  which  the  two  eyes,  acting  conjointly,  recognize 
the  effects  of  binocular  vision  is,  according  to  Briicke, 
Brewster,  and  Provost,  an  incessant  but  unconscious  move- 
ment or  change  of  axis;  and,  according  to  Wheatstone 
and  Dove  and,  to  an  extent,  of  Le  Conte,  not  necessarily 
any  movement  or  change  of  axis  at  all ; and  we  have 
found  that  in  the  degree  in  which  the  contour  of  a form 
is  elliptical  or  even  circular,  rather  than  square  or  rectangu- 
lar, it  can  be  recognized  without  ocular  movement,  or,  at 
least,  conscious  ocular  movement. 

In  the  use  of  the  eyes,  the  difference  between  move- 
ment and  no  movement,  or,  if  the  other  theory  be  adopted, 
between  conscious  movement  and  no  conscious  movement, 
is  the  difference  between  activity,  work,  or  effort,  and  rest, 
play,  or  enjoyment.  Notice  now  that  this  is  the  same  dif- 
ference as,  in  Chapters  VII.  and  VIII.  of  “Art  in  Theory,” 
is  said  to  distinguish  that  which  is  done  with  a utilitarian 
aim  and  an  aesthetic.  But  if  a form  of  outline  naturally 
fitting  into  the  shape  of  an  upright  elliptical  figure,  be 
the  one  which  requires,  to  recognize  it,  the  least  visual 
activity  work  or  effort,  or — what  is  the  same  thing — 
which  is  consistent  with  the  most  rest  play  or  enjoy- 
ment; then  this  form  of  outline  must  be  the  one  most 
conformed  to  the  physiological  requirements  of  the  eye. 
In  other  words — and  this  explains  why  the  term  is  used 
in  this  work — it  is  the  form  most  in  harmony  with  these 
requirements;  therefore  the  most  agreeable,  the  most 
pleasurable,  the  most  “ fitted  to  be  perceived,”  which  is 


SHAPES  PERCEIVED  WITH  LEAST  EFFORT.  283 


the  exact  etymological  meaning  of  the  word  (esthetic.  But 
this  fact  furnishes  the  best  possible  justification  for  calling 


the  curve,— particularly,  as 
we  shall  notice  presently,  the 
one  found  in  the  ellipse, — the 
line  of  beauty. 

What  has  been  thus  found 
to  be  true  with  reference  to 
the  elliptical  contour,  renders 
significant  many  other  facts 
— indeed,  whole  classes  of 
facts  with  which  few  of  us 
can  fail  to  be  familar.  Recall, 
for  instance,  the  extensive  use 
in  art  of  this  elliptical  shape. 
If  we  go  into  the  shops 
where  they  sell  implements 
for  drawing,  whatever  else 
they  may  not  keep,  assortm 
sizes  of  ellipses  are  sure  to  m 


FIG.  117.— EGYPTIAN  DOLL  AND  VASE. 

See  pages  284,  295. 


; of  models  for  different 
our  eyes.  The  one  orna- 


J 1 


FIG.  118.— PRIZE  VASES  FOR  ATHENIAN  GAMES. 

See  pages  284,  295. 


mental  object,  avowedly  not  modelled  after  an  appearance 
in  nature,  which  the  arts  of  all  lands  and  races  have  united 


284 


PROPORTION  AND  HARMONY. 


in  producing,  is  the  vase;  and  this  is  almost  invariably 
conformed  to  vertical  elliptic-lanceolate  outlines.  See  Figs, 
u 7,  page  283,  and  118,  page  283.  Again,  in  architecture, 
the  form  that  general  usage  has  shown  to  be  the  most  sat- 
isfactory is  one  which,  whether  we  consider  it  as  exempli- 
fied in  the  cupola  or  the  dome,  is  like  that  described  within 


FIG.  1 1 9, — BUILDING  ENCLOSED  BY  CIRCLES. 
See  page  284. 


the  space  enclosed  between  circles  in  the  centre  of  Fig.  1 19, 
and  even  if  the  building  be  wide,  the  form  preferred  for 
this  is  one  containing  at  least  a central  part  which,  as  in 
Fig.  1 19,  it  is  possible  to  enclose  in  such  a space.  Of  course, 
there  are  other  reasons  for  the  arrangement  of  the  dome, 
shaped  as  it  is,  in  the  centre  of  such  a building — reasons 
founded  on  the  fulfilment  of  such  principles  as  tinity , 
principality , and  balance,  as  explained  in  Chapters  II.  to 


286 


PROPORTION  AND  HARMONY. 


V.  of  “The  Genesis  of  Art-Form.”  But  these  principles 
do  not  explain  the  particular  shape  of  the  contour  as  a 
whole,  as  does  the  reason  attributing  it  to  ease  of  action 
on  the  part  of  the  eye  when  looking  at  it  as  a whole. 

In  art,  as  in  everything,  there  may  be  more  than  one 
reason  for  an  effect.  D.  R.  Hay,  in  his  interesting  work 
entitled  “ Ornamental  Geometric  Diaper  Designs  accom- 
panied by  an  Attempt  to  Develop  and  Elaborate  the  true 
Principles  of  Ornamental  Design  as  applied  to  the  Deco- 
rative Arts,”  says  of  the  ellipse,  that  it  “ possesses  that 
essential  constituent  of  beauty,  variety.  . . . Its  outline 
being  formed  by  two  radii,  one  of  which  is  continually 
decreasing  while  the  other  is  increasing,  it  imperceptibly 
varies  from  an  oblate  to  an  acute  curve.”  This  statement 
will  be  recognized  to  be  almost  identical  with  the  one  in 
Chapter  XVII.  of  “ The  Genesis  of  Art-Form,”  and  made 
on  page  61  of  this  book  with  reference  to  the  effects  of 
the  kinds  of  curves  which  Ruskin  declares  to  be  the  most 
beautiful  in  nature.  In  accordance  with  the  principle 
which  he  is  unfolding  Mr.  Hay,  in  his  work  just  men- 
tioned, goes  on  to  say  that  “ the  ellipse  the  proportions 
of  which  arise  out  of  the  harmonic  divisions  of  the  circle 
. ...  is  entitled  to  be  termed  the  primary  of  its  class  or, 
in  distinction  to  all  other  forms,  the  ellipse.”  By  this 
ellipse  he  means  one  exactly  described  about  a rectangle 
twice  as  long  as  it  is  wide,  a rectangle,  therefore,  whose 
length  is  to  its  breadth,  or  to  the  length  of  a square  as  2 : i. 
Such  an  ellipse  is  described  by  many  of  the  lines  in  Fig. 
120,  page  285.  That  this  ellipse,  as  well  as  others  based 
upon  exact  multiples  of  the  circle,  fulfils,  in  a peculiar 
sense,  the  requirements  of  the  art-methods  indicated  on 
page  3,  and  of  beauty  as  determined  by  these,  as  well  as 
of  proportion,  as  unfolded  in  Chapters  II.  to  VIII.,  is  cvi- 


ELLIPTICAL  SHAPES. 


287 


dent ; and  the  conclusions  with  reference  to  the  desirabil- 
ity of  its  use  in  geometric  designs  are  sound.  Notice  the 
graceful  and  yet  greatly  varied  curves  through  which, 
when  placed  together  as  in  Fig.  121,  the  outlines  of  such 
ellipses  pass  into  one  another. 

But  Mr.  Hay’s  conclusions  hardly  explain  the  origin  of 
the  ellipse  as  a whole  ; or  why  innumerable  forms  in  na- 
ture, like  those  of  vases,  trees,  and  men,  are  not  consid- 


FIG.  121.— CURVED  LINES  AS  OUTLINED  BY  ELLIPSES. 

See  page  287. 


ered  less  beautiful  than  others  even  though  their  outlines 
are  not  conformed  even  proportionately  to  the  ratios  of 
that  ellipse  which  he  declares  to  be  the  most  beautiful. 
For  instance,  Fig.  120,  page  285,  was  drawn  by  him  to  show 
the  influence  of  this  ellipse  upon  the  forms  of  vases.  The 
dotted  lines  indicate  these  ellipses,  and  the  finer  continu- 
ous lines  the  vases  described  by  him.  To  the  same  fig- 
ures the  heavier  continuous  lines  have  been  added  by  the 
author  of  the  present  volume  to  show  the  shapes  repre- 
sentative of  vases  whose  sides  conform  exactly  to  parts  of 


288 


proportion  and  harmony. 


intersecting  circumferences  drawn  as  exemplified  in  Fig. 
1 16,  page  278.  There  will  probably  be  little  doubt  in  the 
minds  of  any  examining  the  figures,  that  these  heavier 
lines,  fully  as  well  as  the  lighter  continuous  lines  drawn 
by  Mr.  Hay,  represent  the  forms  which  usage  in  all  coun- 
tries has  shown  to  be  most  generally  considered  satisfac- 
tory. To  what  extent  the  contours  of  leaves  and  bushes 
conform  to  this  elliptical-lanceolate  shape  will  be  found 
illustrated  sufficiently  in  Fig.  39,  page  78.  But  a very  in- 
teresting exemplification  of  how  the  same  shape  may  be 
supposed  to  be  seen  in  the  forms  of  animals,  birds,  and 
fishes  may  be  noticed  in  Fig.  122,  page  289.  It  is  copied 
in  Mr.  Hay’s  volume,  already  mentioned,  from  Sir  William 
Jardine’s  “ Naturalist  Library,”  the  birds  representing  the 
cuckoo  and  the  blackbird  ; and  the  fishes  representing  the 
salmon  and  the  turbot.  It  will  be  noticed  that  the  out- 
lines of  many  of  these  are  so  placed  in  nature  that  the 
elliptical  spaces  to  which  their  shapes  are  here  shown  to 
conform  have  their  longest  dimensions  horizontal  rather 
than  vertical  ; and  that,  so  far  as  this  is  the  case,  these 
shapes  do  not  exactly  fulfil  the  principle  illustrated  in 
Fig.  1 16,  page  278.  But  may  we  not,  without  making 
too  much  of  a mere  suggestion,  suppose  this  lack  of  cor- 
respondence to  give  significance  to  the  fact  that,  when 
examining  such  forms  closely,  men  instinctively  turn 
their  heads  first  to  one  side  and  then  to  the  other,  where, 
whatever  may  be  their  real,  not  to  say  conscious  reason 
for  the  movement,  it  is  a fact  that  the  elliptical  space 
will  appear  to  be  in  the  same  upright  position  as  it  is  when 
between  the  overlapping  circumferences  in  Fig.  1 1 6,  on 
page  278  ? Besides  this,  is  it  not  true  that,  when  one  has 
come  to  recognize  an  aesthetically  satisfactory  effect  in  an 
ellipse  prolonged  vertically,  there  is  a tendency,  according 


J9 


289 


2 go 


PROPORTION  AND  HARMONY. 


to  the  laws  of  association,  for  him  to  recognize  the  same 
effect,  even  when  suggested  by  an  ellipse  prolonged  hori- 
zontally? Take,  for  instance,  the  form  of  a man’s  limb — 
not  when  standing  but  when  sitting  down  ; and  in  such 
a position  that  one  can  see  only  a small  part  of  him. 
We  certainly  should  not  admire  this  part,  in  case  it  were 
comparatively  small,  and  we  knew  that,  when  he  stood  up, 
he  would  prove  to  be,  as  a whole,  comparatively  large. 
This  shows  that  the  standard  by  which  we  judge  is  one 
in  which  the  limbs  are  in  their  normal  standing  posture  ; 
and,  when  they  are  not  so,  that  we  form  our  inferences  of 
them  by  way  mainly  of  association. 

This  reference  to  the  human  figure  reminds  us  that  in 
it  alone  do  we  find  the  form  which  is  supposedly  the  most 
perfect  in  nature,  the  form  therefore  which  we  should 
expect  to  find  the  most  perfectly  adjusted  to  this  elliptical 
requirement.  In  order  to  show  that  it  is  so,  as  a fact, 
and,  at  the  same  time,  to  show  this  in  such  a way  as  to 
prevent  any  one’s  imagining  that  the  fact  might  not  be 
true  of  drawings  not  prepared  by  the  author,  none  of  those 
to  which  the  principle  is  applied  in  this  book  have  been 
prepared  by  him.  All  are  copied  from  contours  drawn  by 
others  in  accordance  with  what  they  suppose  to  represent 
perfect  proportions.  Figs.  72,  page  136,  and  73,  page  137, 
show  how  the  form  as  a whole  fits  into  an  elliptic-lanceolate 
shape.  Figs.  31,  page  57,  36,  page  71,  73,  page  137,  and 
74,  page  139,  show  how  different  outlines  of  the  same 
form  fit  into  spaces  formed  between  circumferences  of 
the  same  dimensions  ; and  Figs.  32,  page  58,  and  35,  page 
70,  show  how  the  same  is  true  as  applied  not  only  to  the 
shape  of  the  body  when  the  limbs  are  held  together,  but 
when  it  is  assuming  positions  in  which,  as  in  action,  they 
are  more  or  less  separated. 


THE  ELLIPSE  IN  THE  HUMAN  FORM. 


291 


It  will  be  noticed  that  most  of  the  circles  drawn  about 
each  body  are  of  the  same  size.  This  size,  in  Fig.  72,  page 
136,  as  also,  in  one  instance,  in  Fig.  73,  page  137,  is  de- 
termined by  the  height  of  the  enclosed  space  needed  in 
order  to  take  in  the  whole  form  ; and  in  all  the  other 
figures  by  the  height  needed  in  order  to  take  in  certain 
parts  of  the  form.  One  reason  why  the  circles  drawn  about 
the  same  forms  are  of  the  same  size,  is  connected  with 
the  requirements  of  proportion,  as  indicated  on  page  71. 
Another  reason  is  connected  with  the  requirements  of 
ease  in  the  act  of  perception,  in  accordance  with  the 
principle  mentioned  on  page  282.  Circles  of  the  same  size 
represent  the  same  general  convergence  of  the  eyes’  axes  ; 
and  the  wider  enclosed  space  formed  by  the  intersecting 
of  two  such  circles  may  be  supposed  to  include  the  nar- 
rower space.  In  other  words,  if  in  such  a case,  one  can  see 
both  side  contours  of  a form  inscribable  in  the  wider  en- 
closed space,  he  can  also,  without  changing  the  axes,  see 
both  contours  of  a form  inscribable  in  the  narrower  space. 
Or  if  the  latter  form  necessitates,  at  times,  a different  con- 
vergence, when  this  takes  place  by  shifting  attention  from 
one  contour  inscribable  in  a wider  to  another  inscribable 
in  a narrower  space,  and  so  on  by  regularly  graded  de- 
grees, as  in  passing  the  eye  downward  from  the  shoulders 
to  the  shins  of  the  form  in  Fig.  31,  page  57,  or  Fig.  73, 
page  1 37,  this  condition  may  be  supposed  to  represent  the 
least  possible  expenditure  of  visual  effort.  In  fact  the 
tapering  of  the  whole  form,  as  in  these  two  figures,  and  of 
some  of  the  limbs,  very  accurately  fulfils  the  requirements 
of  ease  of  vision  as  mentioned  on  page  237.  According  to 
these  requirements,  the  parallel  vertical  lines  below  the 
horizontal  level  of  the  eyes  at  the  point  in  the  perpen- 
dicular at  which  we  are  looking  have  a tendency  to 


292 


PROPORTION  AND  HARMONY. 


approach  one  another.  This  is  one  explanation  of  the 
satisfactory  effect  produced  by  the  tapering  downward  of 
the  whole  form,  as  well  as  of  the  arms  and  legs  and  dif- 
ferent sections  of  these,  in  all  cases  in  which  they  are  seen 
in  their  normal  upright  position. 

It  was  noticed  on  page  61,  that  besides  like  circles,  like 
curves  of  a more  varied  and  intricate  character  can  be 
drawn  about  the  forms,  causing,  though  with  differing 
widths  and  lengths,  the  same  general  effects  in  the  out- 
lines of  the  arms  from  shoulders  to  elbows,  as  also  of  the 
same  from  elbows  to  wrists;  and  of  the  legs  from  hips  to 
knees,  as  also  of  the  same  from  knees  to  ankles ; as  well,  too, 
as  of  a larger  part  of  the  form  both  from  hips  to  heels  and 
from  shoulders  to  heels.  In  connection  with  this,  the 
presence  was  pointed  out  of  a similar  curve  in  the  arm 
just  below  the  elbow,  in  the  thigh  just  below  the  hip,  and 
in  the  calf  just  below  the  knee — a reason  for  the  aesthetic 
effects  of  which  curve  was  suggested  in  accordance  with 
the  principles  of  proportion.  Here  it  may  be  interesting 
to  consider,  as  an  additional  explanation,  that  this  same 
curve  may  be  supposed  to  describe  exactly  a direction 
according  with  the  most  gradual  changes  in  the  lenses  of 
the  eyes,  when  they  are  looking  from  one  to  another  part 
of  the  form.  Fig.  123,  page  293,  will  crudely  suggest  why 
this  is  so  ; and,  in  suggesting  it,  will  also  suggest  a prin- 
ciple necessarily  more  or  less  applicable  whenever  the 
eyes  in  glancing  up  or  down  the  contour  of  a form  are 
obliged,  for  the  reason  mentioned  on  page  280,  to  adjust 
outlines  to  backgrounds  at  different  distances.  Let  the 
circle  A B represent  the  general  field  of  vision  of  both 
eyes  when  looking  at  some  point  on  a straight  line  supposed 
to  be  drawn  between  a and  b.  If  then  attention  be 
directed  first  upon  a , and  from  it  passed  upward  to  b, 


CURVES  A CCOM MOD  A TED  TO  E YES. 


293 


and,  while  this  is  being  done,  the  circle  representing  the 
field  of  vision  of  one  eye  be  gradually  pulled  apart  from 
the  circle  representing  the  field  of  vision  of  the  other 
eye  (which  would  represent  what  is  done  when  the  eyes 
are  adjusting  their  lenses  to  a more  distant  background) 
then,  instead  of  the  one  circle  A B,  we  should  have  the 


D B C 


FIQ.  123.— OUTLINES  OF  CURVES  AS  DETERMINED  BY  CHANGES  IN  BACKGROUNDS. 

See  pages  292,  293,  294,  295. 

two  circles  under  Cand  D,  and  instead  of  the  one  straight 
line  between  a and  b,  we  should  have,  as  representing  the 
appearance  which  the  eyes  could  perceive  with  the  least 
change  of  focus,  and  therefore  with  the  least  effort,  the 
contour  indicated  by  the  dotted  lines  between  a and 
b.  Or  suppose,  when  the  general  field  of  vision  of  the 
two  eyes  may  be  represented  by  A B,  and  they  be 
looking  in  a general  way  at  the  figure  indicated  by  the 
undotted  lines  between  a and  b,  that  attention  be  directed 
upon  a and  passed  upward  along  the  sides  of  this  figure 


2Q4 


PROPORTION  AND  HARMONY. 


to  b,  and,  while  this  is  going  on,  that  the  circle  A B be 
gradually  pulled  apart  so  as  to  form  the  two  circles  under 
C and  D,  then  the  figure  now  represented  in  the  one  circle 
A B by  the  undotted  lines  between  a and  b would  in  the 
two  circles  under  C and  D be  perceived  with  the  least  effort 
when  assuming  the  form  represented  by  the  dotted  lines 
between  a and  c and  a and  d.  Or,  if  we  suppose  that,  in 
exactly  the  same  time,  the  eyes  glance  from  a toward 
c or  d,  but  finally  to  rest  on  B,  then  the  figure  repre- 
sented by  the  dotted  lines  between  a and  B,  would  be 
perceived  with  the  least  effort.  Once  more,  if  we  suppose 
attention  to  be  directed  upon  A and  started  around 
either  side  of  the  circumference  toward  B;  then,  while 
the  one  circle  A B is  being  gradually  extended  into  the 
two  under  C and  D,  it  will  be  the  outlines  indicated  by 
the  dotted  lines  between  AC  and  A D,  that  the  eyes  will 
perceive  with  the  least  effort.  The  courses  of  the  dot- 
ted lines  in  this  Fig.  123,  are  determined  by  measuring  the 
whole  height  and  the  whole  breadth  of  the  space  to  be 
covered,  and  passing  the  dotted  lines  through  the  points 
representing,  say  one  eighth  of  the  height,  and  also  repre- 
senting at  the  same  time  one  eighth  of  the  breadth  and  after 
that  one  fourth  of  each,  and  so  on.  In  other  words,  the  dis- 
tances of  the  dotted  lines  from  the  undotted  ones  is  always 
graded  according  to  an  exact  ratio  of  measurement  between 
the  height  and  the  breadth.  The  dotted  lines,  therefore, 
represent  results  the  same  in  principle  as  those  of  pro- 
portion. It  will  be  noticed,  moreover,  that  in  all  cases 
these  lines  resemble  more  or  less  closely  those  represented 
in  Figs.  33,  page  60,  and  34,  page  61.  They  therefore  sug- 
gest, in  addition  to  what  was  said  on  page  6f,  why  such 
curves  should  be  characteristic  of  grace  in  visible  move- 
ments, or  in  fixed  lines  which  the  eye,  through  its  own 


CURVES  ACCOMMODATED  TO  EYES.  295 

movements,  has  to  trace  from  one  part  of  a figure  to 
another.  It  will  be  noticed,  too,  that,  somewhere  between 
the  different  gradations  of  contours  between  dotted  a — b 
and  a — B we  can  find  contours  to  represent  all  the  forms 
most  readily  suggested  by  the  configurations  of  arms,  legs, 
hips,  or  the  whole  framework  of  the  human  body  as 
indicated  in  Figs.  31,  page  57;  32,  page  58;  35,  page  70; 
36,  page  71  ; 37,  page  72;  45,  page  86;  72,  page  136;  73, 
page  137;  and  74,  page  139,  to  say  nothing  of  Figs.  117, 
page  283  ; 1 18,  page  283  ; 120,  page  285,  and  122,  page  289. 
But  enough.  The  applications  of  Fig.  123,  page  293, 
would  be  made  to  conform  more  to  all  cases  if  the  circles 
under  C and  D were  also  represented  as  being  elevated 
and  enlarged  at  the  same  time  as  being  pulled  apart ; and 
if,  in  addition  to  considering  effects  due  to  adjusting  the 
lens  of  the  eye,  horizontally,  those  were  considered  which 
are  due  to  its  convex  shape,  as  well  as  to  the  rotary  action  of 
the  whole  eye  while  moving.  But  the  object  of  this  dis- 
cussion has  been  merely  to  unfold  a general  principle.  It 
is  evident  that  none  of  these  considerations  would  change 
this  principle,  however  much  they  might  extend  its  scope, 
or,  by  conflicting  conditions,  modify  its  applications.  Be- 
sides this,  the  subject  itself  is  a large  one,  and  in  the 
present  state  of  knowledge  concerning  it,  any  thorough 
treatment  of  it  would  demand,  if  not  a mathematical 
genius,  at  least  a man  with  less  to  do,  and  with  less  inter- 
est in  other  directions  than  the  author  of  this  volume.  He 
must  be  content  with  these  few  suggestions,  and  leave  to 
others  whatever  possibility  there  may  be  of  developing 
from  them  anything  like  a complete  system  of  geometric 
aesthetics. 


CHAPTER  XVII. 


ARTISTIC  COLORING  AS  INFLUENCED  BY  SCIENTIFIC 
METHODS. 

Imitative  and  Decorative  Use  of  Color — The  Two  Connected — Scientific 
Study  of  Color  Important — Art  can  Advance  beyond  the  Discoveries 
of  Science — Yet  in  Every  Age  is  Helped  by  Them — Artistic  Invention 
as  Related  to  Scientific  Investigation  of  Effects  of  Color — Illustrated 
from  History  of  Greek  Painting — Roman — Christian — Italian — Spanish 
and  Dutch — English — French — German — Modern — Need  of  Learning 
from  Experience  and  Experiment. 

'HERE  are  two  methods  of  using  color,  one  having 
to  do  with  imitating  it  so  as  to  represent  it  as  we 
find  it  in  certain  agreeable  or  beautiful  appearances  of 
nature  ; the  other  with  applying  or  arranging  it,  irrespec- 
tive of  anything  but  the  general  principles  in  accordance 
with  which  it  appears  to  be  agreeable  or  beautiful.  As 
painting  gives  us  pictures  of  the  forms  of  nature,  and 
architecture  does  not,  it  is  natural  to  suppose  that  the 
first  of  these  methods  is,  or  should  be,  used  mainly  in  the 
former  art,  and  the  second  mainly  in  the  latter,  i.  e.,  in 
the  decoration  of  the  interiors  or  exteriors  of  buildings. 
This  natural  supposition  it  would  be  well  if  some  of  our 
modern  painters  would  ponder.  When  they  imagine  that 
they  can  use  color  merely  “ for  its  own  sake  ” they  are 
on  ground  almost,  though  not  quite,  as  dangerous — 
owing  to  the  far  more  subtle  requirements  of  color  when 
used  in  any  circumstances  whatever — as  are  poets  who 
imagine  that  they  can  use  rhyme,  or  any  other  element 

296 


COLORING  AS  RELATED  TO  SCIENCE . 2Q7 

of  sound,  merely  “ for  its  own  sake.”  The  primary  ob- 
ject of  both  painting  and  poetry  is  to  represent  certain 
effects  that  are,  or  that  may  be  supposed  to  be,  in  nature  ; 
and  the  moment  that  this  primary  object  is  forgotten  the 
artist  or  author  has  crossed  the  boundaries  of  his  own  art, 
and  must  compete  with  the  decorators  or  musicians,  in 
circumstances  where  imitative  limitations  by  which  they 
are  not  hampered  will  materially  interfere  with  his  success. 

It  must  not  be  supposed,  however,  that  the  painter, 
while  subordinating  his  arrangements  of  color  to  effects 
of  nature,  has  no  more  to  do  than  to  imitate  these,  even 
though  our  conception  of  imitation  include  its  greatest 
breadth  and  dignity  of  meaning.  In  Chapter  IV.  of  “ Art 
in  Theory,”  it  was  argued  that  the  aim  of  high  art  is 
never  mere  imitation  ; and  the  truth  of  the  statement  is 
nowhere  exemplified  more  clearly  than  when  applied  to 
the  use  of  color.  Merely  because  blue  in  the  natural 
spectrum  stands  between  green  and  purple,  is  no  proof, 
as  we  shall  find  by-and-by,  that  a blue  object  should  be 
represented  in  a painting  as  standing  next  to  one  that  is 
green  or  violet.  In  the  natural  spectrum,  as  in  a natural 
scene,  bounded  by  only  the  horizon,  there  are  other  coun- 
teracting, balancing,  or  complementary  influences  of  color, 
which  may  render  an  effect  entirely  different  from  that 
which  alone  is  possible  where  a few  colors  are  introduced 
into  the  narrow  framework  of  a picture.  Besides  this,  the 
mere  association  of  certain  hues  in  nature  does  not  make 
the  arrangement  beautiful  ; and,  if  not,  art  has  no  business 
to  reproduce  it.  For  both  reasons,  it  must  always  be 
borne  in  mind  that  art  deals  with  selected  colors,  just  as 
poetry  and  music  deal  with  selected  tones  ; and  harmony 
in  all  these  arts,  though  discovered  from  a study  of  prin- 
ciples in  nature,  is  distinctively  a human  invention.  The 


298 


PROPORTION  AND  HARMONY. 


same  general  principles  of  harmony,  too,  apply,  as  has 
been  said,  though  with  a different  aim,  in  both  painting 
and  decoration.  Therefore  it  will  not  be  necessary  to 
separate  the  two  departments  in  our  discussion,  a few 
references,  here  and  there,  to  the  differences  between 
them  being  sufficient. 

What  has  been  said  of  the  necessity  of  harmony  in 
color,  will  serve  to  obviate  the  impression,  if,  indeed,  it 
exist  in  any  mind,  that  the  scientific  study  of  the  subject 
is  not  essential  to  the  painter.  It  is  true  that  he  can  de- 
pend for  his  copy  upon  nature  to  an  extent  which  is  not 
true  of  the  decorator.  But  nature  is  a very  broad  term. 
What  is  in  it,  cannot  be  thoroughly  perceived  without  a 
good  deal  more  than  mere  superficial  observation.  In 
view  of  the  few  great  colorists  that  the  world  has  known, 
it  is  certainly  no  idle  question  whether  more  attention  to 
the  underlying  principles  of  the  subject  would  not  have 
made  others  more  successful. 

Not,  of  course,  that  one  would  wish  to  intimate  that  the 
arts,  in  certain  cases,  are  not  able  to  advance  without  the 
aid  of  science.  As  a fact  they  often  anticipate  the  discover- 
ies of  this  by  many  centuries,  the  intuitions  of  great  artists 
being  a better  guide  to  achievement  than  the  inferences 
of  the  logicians.  As  A.  J.  Symington  has  shown  in  the 
second  volume  of  his  work  on  “ The  Beautiful  in  Nature, 
Art  and  Life,”  a Crystal  Palace  was  built  by  Chaucer’s 
imagination  in  his  “ House  of  Fame,”  years  before  com- 
mercial enterprise  and  engineering  skill  had  devised  the 
one  at  Sydenham. 

“ But  as  I slept,  me  mette  I was 
Withyn  a temple  ymade  of  glas  ; 

In  whiche  there  were  moo  ymages 
Of  golde  standynge  in  sondry  stages, 


GREAT  PAINTERS  SCIENTIFIC  DISCOVERERS.  299 


And  moo  ryche  tabernacles 
And  with  perrie  moo  pynacles 
And  moo  curiouse  portraytures, 

And  queynt  maner  of  figures, 

Of  golde  werke,  than  I ever  sawgh,”  etc. 

“ In  this,”  says  Mr.  Symington,  “ we  have  mention  of 
the  assembling  together  of  all  nations  in  a wondrous  tem- 
ple made  of  glass,  containing  works  of  industry  and  treas- 
ures of  art  ; with  details  of  its  sculpture,  and  portrait 
galleries,  its  rich  carvings  and  jewellery,  the  indescribable 
variety  of  its  splendors  within,  and  the  glorious,  far-stretch- 
ing landscape  without.  We  have  even  ‘ a noble  Queen  ’ 
seated  on  the  dais  and  awarding  honors  to  worthy  com- 
petitors, the  whole  affording  another  striking  illustration 
. . . . that  the  germs  of  all  inventions  or  discoveries, 

like  the  tulip  in  the  bulb,  already  exist  in  the  mind  of 
man  as  possibilities,  frequently  finding  expression  ages 
before  they  are  realized.” 

Notwithstanding  his  occasional  prescience,  however,  the 
artist,  like  every  one  else,  is  “ the  heir  of  all  the  ages.” 
The  principles  taught  him  and  exemplified  in  the  pro- 
ducts around  him,  have  been  gradually  learned  by  patient 
thought,  investigation,  and  experience  continued  through 
centuries.  And  there  is  still  more  to  be  learned.  Indeed, 
with  reference  to  the  very  subject  with  which  we  are  now 
dealing,  in  no  age  have  more  discoveries  been  made  than 
in  our  own.  And  the  artist  of  to-day  whose  name  will 
live  longest  will  probably  be  he  who  is  the  most  nearly 
able  to  make  as  good  use  of  what  is  known  now,  as  Leo- 
nardo and  Titian  made  of  what  was  known  in  their  times, 
contributing  as  they  did  from  their  very  limited  resources 
what  has  proved  to  be  of  lasting  value  not  only  to  the  art 
of  the  subject  but  also  to  its  science. 


300 


PROPORTION  AND  HARMONY. 


In  the  history  of  the  use  of  pigments  especially,  has  the 
connection  been  very  intimate  between  the  study  of  the 
subject  as  a science,  and  the  development  of  it  as  an  art. 
With  scarcely  an  exception,  the  greatest  painters  seem  to 
have  attained  to  fame  almost  as  much  on  account  of  their 
discoveries  as  of  their  productions,  the  inspiration  to 
investigation  having  apparently  proved  the  surest  stimu- 
lus to  invention.  At  least,  it  can  be  said  that  the  two 
tendencies  have  gone  hand  in  hand  ; and  undoubtedly 
the  frequent  temporary  decline  of  painting,  as  of  every  art, 
immediately  after  great  achievements,  has  been  attributa- 
ble in  part  to  the  supposition  of  men  of  genius  that  all  its 
secrets  had  been  discovered, — a supposition  which  has 
caused  them  to  turn  from  it  to  pursuits  like  philosophy, 
science,  or  politics,  which  seemed  at  the  time  to  promise 
a more  certain  reward  for  original  effort. 

The  briefest  review  of  the  history  of  painting — exclud- 
ing modern  whose  rank  is  not  yet  determined — will  reveal 
the  connection  just  indicated.  The  pictures  of  the  Greeks 
have  perished,  but  from  what  we  read  of  them  there  seems 
to  be  little  doubt  that,  after  the  century  preceding  that 
of  Pericles  in  which  the  unshaded  colors  of  the  Egyptian 
style  were  imitated  in  the  historical  paintings  of  Aglao- 
phon,  and  his  son  Aristophon,  as,  later,  in  the  wall-deco- 
rations of  Damophilus  and  Gorgasus  at  Rome,  the  art 
began  to  be  studied  scientifically.  Pliny  tells  us  that 
the  painters  Micon  and  Polygnotus  improved  the  mate- 
rials used  in  pigments  ; that,  in  the  same  age,  Panaenus, 
a nephew  of  Pheidias,  invented  a new  vehicle  for  fresco. 
Apollodorus,  in  the  age  that  followed,  is  said  by  Plu- 
tarch to  have  been  the  “ first  of  men  to  discover  the 
mixture  of  pigments  and  the  gradations  of  shade.”  Eu- 
pompus,  his  contemporary,  as  well  as  Pamphilus  in  the 


GREAT  PAINTERS  SCIENTIFIC  DISCOVERERS.  3OI 

next  generation,  is  called  a scientific  teacher  as  well  as  a 
painter.  Euphranor,  although  he  had  as  rivals  Zeuxis,  the 
great  master  of  still  life,  and  Parrhasius,  who  “ first  gave 
symmetry  ” and  “ liveliness  of  expression  ” to  figures,  and 
“ won  the  palm  in  terminating  lines,”  surpassed  both,  we 
are  told,  in  his  coloring.  The  body  of  his  Theseus  was 
not  “rose  color,”  it  is  said,  “but  real  flesh.”  Finally, 
when  we  come  to  the  culminating  age  of  Greek  paint- 
ing, that  of  Alexander  the  Great,  we  read  that  although 
Protogenes  excelled  in  ideality,  Nicomachus  in  facility, 
Nicias  in  shading  and  projecting  figures  from  a back- 
ground, and  Pausias  in  foreshortening  and  encaustic  paint- 
ing, Apelles  surpassed  them  all,  not  merely  on  account 
of  his  accuracy  in  drawing  and  his  judgment  in  secur- 
ing the  best  expressions,  but  on  account  of  his  skill 
in  using  colors.  He  brought  out  and  softened  them  with 
a thin  coating  of  black  pigment  that  no  one  could  suc- 
ceed in  imitating.  “He  painted,”  wrote  Pliny,  “what 
could  not  be  painted,  sheet  lightning,  chain  lightning  and 
heat  lightning.”  1 

After  Apelles,  we  read  of  a few  Greeks  or  Romans  like 
Pyreicus  and  Fabius  (b.C.  300)  and,  near  the  beginning  of 
the  Christian  era,  of  Fabullus,  Dorotheus,  Pinus,  and 
Turpilius,  and  later  of  Artemidorus  (a.D.  ioo),  Aristo- 
demus  (a.D.  150),  Hermogenes  (a.D.  250),  and  Hilarius 
(a.D.  365),  but  of  no  new  discoveries,  and,  for  this  reason 
apparently,  of  no  great  artists.  The  paintings  after  this 
period,  up  to  that  of  the  Renaissance,  were  chiefly,  so  far 
as  concerned  the  use  of  color,  of  the  decorative  kind,  de- 
signed to  set  off  the  architecture  of  a church,  or  to  increase 
the  impressiveness  of  an  altar.  Their  backgrounds  were 

1 See  Pliny’s  “ Nat.  Hist.,”  xxxiii.,  13,  56  ; xxxiv.,  8,  19  ; xxxv.,  6,  25  ; 
8,  34 ; 9,  36  ; 11  ; 12,  45  ; also  Plutarch’s  “ In  Gloria  Athen.,”  2. 


302 


PROPORTION  AND  HARMONY. 


usually  gilded,  and  the  drapery  of  their  figures  was  com- 
posed of  full  colors,  red,  blue,  or  yellow,  and  little  varied, 
while  different  parts  of  the  hands  and  faces,  which  were 
sadly  out  of  proportion,  were  indicated  by  black  lines, 
such  as  caricaturists  of  our  own  time  would  use  for  a simi- 
lar purpose. 

At  last,  between  the  thirteenth  and  fifteenth  centuries, 
Cimabue,  Giotto,  Orcagna,  Lippi,  Masaccio,  Perugino  and 
others,  among  whom  Gentile,  merely  because,  as  the  prede- 
cessor, some  suppose  him  to  be  the  founder  of  the  Vene- 
tian school  of  colorists,  ranks  well,  prepared  the  way  in  Italy 
for  the  advent  of  Leonardo  da  Vinci.  The  latter  applied 
himself  to  the  task  of  representing  with  literal  truth  just 
what  he  saw  in  nature,  and  succeeded  in  drawing-  figures 
and  drapery  that  looked  like  those  of  life.  In  the  treat- 
ment of  his  coloring  there  was  a gradation,  too,  that  had 
not  been  seen  in  the  works  of  his  predecessors,  notwith- 
standing much  excellence  that  they  had  exhibited,  espe- 
cially in  the  way  of  flesh  tints.  Immediately  after  Leo- 
nardo, came  three  painters  deemed  by  some  the  greatest 
that  have  ever  lived,  Michael  Angelo,  excelling  in  his 
knowledge  of  anatomy,  and  in  the  grasp  and  grandeur  of 
his  designs,  Raphael  in  the  expressive  grace  and  beauty 
of  his  forms  and  faces,  and  the  dramatic  character  of  his 
compositions,  and  Titian  in  his  use  of  color.  These 
three  lived  at  a time  when  they  could,  as  they  did,  make 
original  contributions  to  their  art ; though  it  is  true 
that  only  the  latter  made  them  distinctively  in  the  sphere 
which  we  are  now  considering.  Titian  was,  in  the  strictest 
sense  of  the  term,  a great  painter ; though  his  works 
were  also  characterized  by  force  and  refinement  of  drafts- 
manship. Among  other  things  he  developed  the  effects 
of  contrast  between  the  light  and  dark  hues.  He  did 


GREAT  PAINTERS  SCIENTIFIC  DISCOVERERS.  303 


this,  however,  in  a more  limited  way  and  with  a less  intel- 
ligent use  of  the  difference  between  the  cold  and  warm 
colors  than  was  developed  subsequently  by  the  painters 
of  the  Netherlands.  He  taught  that  shadows  are  not 
merely  darker  shades  of  the  colors  casting  them,  but  are 
different  from  them,  and  above  all  that  effective  composi- 
tion must  have  breadth,  yet  softened  by  gradation,  i.  e., 
must  have  massings  in  large  quantities  of  light  and  shade, 
yet  passing  into  one  another  by  degrees,  as  illustrated  in 
Chapters  XIII.  and  XVII.  of  “ The  Genesis  of  Art-Form.” 
(See  also  Fig.  129,  page  359.)  With  the  greatest  of  the  Ve- 
netians we  are  accustomed  to  associate  the  other  promi- 
nent painters  of  his  school,  namely,  his  predecessors,  Bel- 
lini and  Giorgione,  and  his  successors,  the  two  Palmas, 
Tintoretto,  and  Paul  Veronese.  While  Titian  was  still 
living,  Correggio  of  Parma,  born  A.D.  1494,  had  gone 
beyond  him  in  his  development  of  the  possibilities  of 
light  and  shade,  or  of  chiaroscuro,  as  it  is  called,  involving 
a thorough  study  of  gradation  as  applied  to  color.  For 
this  reason,  as  well  as  because  of  the  idealized  beauty  of 
the  faces  in  his  pictures,  he  ranks  very  high.  After  these 
men,  we  have  in  Italy,  beginning  half  a century  later,  the 
eclectic  painters  of  religious  subjects,  the  three  Caracci, 
Domenichino,  Guido,  and  Carlo  Dolci,  who,  acknowledg- 
ing themselves  to  be  imitators,  strove  to  combine  the 
excellencies  of  their  predecessors ; and  the  naturalists, 
Caravaggio,  born  A.D.  1569,  who  turned  from  religious  to 
secular  subjects,  and  Salvator  Rosa,  born  A.D.  1615,  who 
excelled  in  landscapes. 

In  Spain,  Velasquez,  born  A.D.  1599,  was  the  first  to 
perceive  and  attempt  such  atmospheric  color-effects  as  are 
mentioned  on  page  307.  He  is  credited,  too,  with  using  his 
brush  with  as  much  delicacy,  force,  and  precision  as  others 


304 


PROPORTION  AND  HARMONY. 


did  the  pencil;  while  De  Cespedes,  born  A. D.  1538,  and 
Murillo,  born  A.D.  161 5,  celebrated  for  finished  coloring 
and  sweet  grace  of  style,  reproduced  the  effects  in  chiar- 
oscuro of  Correggio.  But  few  would  say  that  the  latter’s 
imitators  rank  quite  as  high  as  he,  and  this,  apparently, 
because  they  did  not  add  essentially  to  his  discoveries. 

Among  the  Dutch  painters,  the  two  Van  Eycks,  who, 
about  A.D.  1390,  started  the  Flemish  school,  invented  oil- 
painting,  and  designed  landscapes,  as  well  as  large  religious 
compositions,  in  which  there  was  a sincere  and,  for  that 
time,  an  original  endeavor  to  represent  the  effects  of  nature. 
Though  producing  nothing  which,  in  these  days,  would  be 
considered  excellent,  they  are  still  highly  esteemed,  as  is 
also  their  most  eminent  follower,  Hans  Memling,  born 
about  A.D.  1430.  The  Flemish  painter  Rubens,  born  A.D. 
1 577,  was  the  legitimate  and  foremost  successor  of  the 
great  Italians,  especially  of  the  Venetians,  whose  works  he 
studied  in  their  native  cities.  He  applied,  as  had  not 
been  done  before,  their  gorgeous  coloring  and  their  har- 
mony of  light  and  shade  to  every  variety  of  subject,  land- 
scape, animal  and  human,  religious,  historical,  and  secular. 
His  followers  developed,  beyond  anything  that  had  been 
done  by  the  Italians,  the  contrasts,  to  be  presently  ex- 
plained, between  the  warm  and  cold  colors,  using  broken 
or,  what  is  the  same  thing,  pale  colors  extensively,  almost 
exclusively,  and  making  much  of  slight  variations  in  them. 
The  foremost  among  these  followers  were  Van  Dyck,  born 
A.D.  1599,  a painter  of  a style  similar  to  that  of  Rubens, 
with  less  force  and  more  sweetness;  Teniers,  the  origina- 
tor of  the  very  successful  Belgian  school  of  genre  painting  ; 
and  Rembrandt,  born  A.D.  1607,  who,  notwithstanding 
the  inferiority  of  some  of  his  subjects  taken  from  real  life, 
is  a Flemish  Correggio,  with  a development  beyond  the 


GREAT  PAINTERS  SCIENTIFIC  DISCOVERERS.  305 


Italian  which  all  of  his  school  manifest.  Many  of  his  ex- 
cellencies, too,  are  shared  by  his  contemporaries  and  suc- 
cessors, men  like  Franz  Hals,  Bol,  Douw,  and  Maas; 
Ruysdael,  celebrated  for  his  landscapes ; Wouvermanns, 
for  his  hunting  scenes  ; and  Van  der  Velde,  for  his  marine 
views. 

English  painting,  like  everything  else  springing  from 
that  country,  has  managed  to  manifest  the  characteristics 
of  the  English  people.  Their  enjoyment  of  domestic  life 
has  led,  from  the  time  of  Hogarth,  born  A.D.  1697,  to  that 
of  Wilkie  and  others  of  our  own  century,  to  a line  of 
original  painters  of  domestic  fiction  ; their  pride  of  ances- 
try to  portrait  and  historical  painters,  like  Reynolds, 
Gainsborough,  Opie,  Lawrence,  Raeburn,  Romney,  and 
Etty  ; and  their  delight  in  country  scenery  to  landscape 
painters  like  Constable  and  Turner.  The  fame  of  the 
last  of  these  once  promised  to  surpass  that  of  all  the 
others.  To  some  extent  these  others  were  imitators. 
He  certainly  was  not  one,  either  in  his  mode  of  coloring 
or  of  blending  literalness  with  ideality.  It  is  the  school 
of  water-colors,  however,  founded  by  Sandby  and  others 
about  A.D.  1750  and  still  flourishing,  which  has  given  to 
England  its  chief  reputation  among  foreign  artists  ; be- 
cause by  this  school  it  is  felt  that  the  country  has  made 
its  chief  original  contribution  to  the  progress  of  the  art. 

In  France,  Poussin,  born  A.D.  1594,  united  the  results 
of  the  Italian  and  Flemish  schools.  Claude  Lorraine, 
born  A.D.  1600,  developed  an  original  way  of  producing 
atmospheric  effects  in  landscapes, — hence  his  reputation. 
His  method  consisted  in  increasing  by  delicate  grada- 
tions the  strength  of  the  light  in  the  centre  of  a hazy  back- 
ground where  the  sun  was  usually  represented  ; and  against 
the  background,  apparently  at  an  infinite  distance  from 


PROPORTION  AND  HARMONY . 


306 

it,  the  trees  and  buildings  of  the  foreground  were  made  to 
stand  out  as  if  in  a silhouette.  From  the  time  of  Claude 
to  the  middle  of  the  present  century,  notwithstanding  the 
great  reputation  at  one  time  attained  by  Lesueur,  born 
A.D.  1617,  with  his  religious  subjects,  by  Joseph  Vernet, 
born  A.D.  1714,  with  his  landscapes,  by  Greuze,  born  A.D. 
1725,  with  his  genre  pictures,  by  the  “classical”  David, 
by  the  “eclectic”  Delaroche,  both  of  the  period  following 
the  Revolution,  as  well  as  by  Gros,  born  A.D.  1771,  and 
by  Horace  Vernet,  born  A.D.  1789,  with  their  historical 
paintings,  perhaps  it  can  be  said  with  truth  that  no  one 
has  secured  more  permanent  renown  than  the  “ romantic  ” 
Delacroix ; and  that  this  has  been  largely  secured  because 
of  the  thorough  study  that  he  is  known  to  have  made  of 
the  subject  of  color. 

In  Germany, — previous  to  the  time  of  Claude, — Diirer, 
Cranach,  and  Holbein,  the  latter  much  the  ablest  of  the 
three,  who  all  flourished  in  the  fifteenth  century,  had  pro- 
duced works  which  rank  with  the  best  of  those  of  Italy 
before  the  time  of  Leonardo.  Many  years  later,  Raphael 
Mengs,  born  A.D.  1728,  a special  friend  of  the  great  art 
critic,  Winckelmann,  became  head  of  the  Academy  of 
Florence.  Overbeck,  born  A.D.  1789,  tried  to  produce 
sacred  pictures  like  the  great  Italians,  and  had  no  little 
indirect  influence  in  inclining  towards  a similar  object 
the  pre-Raphaelite  movement  in  England.  Cornelius, 
born  A.D.  1783,  together  with  Schadovv,  restored  historic 
fresco,  and  inspired  much  that  was  popular  in  the  Acade- 
mies of  Dusseldorf  and  Munich,  in  both  of  which  Cornelius 
taught.  Subsequently  Lessing  and  Bendemann  applied 
the  methods  of  Overbeck  and  Cornelius  to  non-Romish 
subjects,  and  Ivaulbach,  who  died  A.D.  1874,  left  behind 
him  a well  earned  reputation  for  the  force  and  grasp  of 


GREAT  PAINTERS  SCIENTIFIC  DISCOVERERS.  307 


his  drawing  and  composition.  None  of  these,  however, 
were  masters  of  the  art  of  coloring,  much  less  discoverers 
of  anything  new  with  reference  to  it.  And  it  is  significant, 
therefore,  that,  as  compared  with  successors  who  are  better 
colorists,  the  reputation  of  all  pf  them  is  declining. 

Within  the  last  half-century,  the  art  of  painting,  accord- 
ing to  some  of  our  foremost  authorities,  has  been  almost 
revolutionized  ; and  here  again  we  have  to  attribute  the 
result  to  a change  in  the  methods  of  producing  effects  in 
color.  The  older  painters,  as  a rule,  mixed  their  hues 
before  placing  them  on  the  canvas,  and  put  them  there 
exactly  as  they  wished  to  have  them  appear  when  seen 
from  a distance.  Velasquez  introduced  another  method 
which,  of  late,  modern  painters  have  been  developing. 
According  to  it,  colors  are  placed  on  the  canvas  so  that, 
tho  not  mixed,  they  shall,  when  seen  from  a distance,  mix  in 
the  eye.  This  is  the  way  in  which  the  color-effects  of  na- 
ture are  usually  produced  ; and  the  method,  in  many  cases, 
renders  the  art-product  much  more  satisfactory,  suggesting 
that  the  elements  entering  into  a scene,  like  those  of 
leaves  and  grasses,  are  separated  from  one  another,  and 
thus  conveying  impressions  of  transparency  and  atmos- 
phere, which  were  impossible  according  to  the  older 
method.  As  in  the  case  of  every  “ good  thing,”  however, 
this  method  is  often  carried  too  far.  Certain  absurd  ex- 
tremes of  impressionism  are  developments  that  never 
would  have  had  existence  but  for  what  is  true  in  it;  and 
the  same  may  be  said  of  the  equally  absurd  conception 
that  a smooth  surface,  as  in  the  human  countenance,  re- 
quires no  different  treatment  from  that  which  would  be 
afforded  the  rough  surface  of  a flower-bed.  At  the  same 
time,  the  general  effect  of  having  colors  mix  in  the  eye, 
with  the  attendant  impressions  conveyed  of  transparency 


308 


PROPORTION  AND  HARMONY. 


of  atmosphere,  and  of  infinity  in  gradations  seems  to  be  ac- 
cepted as  a crucial  test  of  excellence  in  modern  painting. 
It  is  safe  to  say  that  the  Fontainebleau-Barbizon  and  the 
Spanish-Roman  schools,  which  have  been  chiefly  instru- 
mental in  introducing  these  new  methods,  have  changed 
the  whole  character  of  much  of  the  contemporary  art  in 
other  countries,  and  of  all  of  that  in  our  own.  The  former 
school  has  led  to  results  mainly  in  the  deeper  tones  of 
color,  such  as  we  find  in  the  works  of  Rousseau,  Corot, 
Troyon,  Diaz,  and  Millet,  and  the  latter  to  those  largely  in 
the  higher  tones,  such  as  we  find  in  the  works  of  Fortuny, 
Zamagois,  Boldini,  Rico,  and  Villegas.  As  a master  of 
composition,  Gerome  has  no  equal,  and  he  as  well  as 
Cabanel,  Bouguereau,  and  Baudry,  surpass  those  just  men- 
tioned in  effects  of  draftsmanship.  But  notwithstanding 
this,  it  is  the  others  of  whom  we  hear  most,  and  who  have 
had  the  most  imitators.  Thus,  at  present,  as  in  the  past, 
the  fact  which  this  brief  review  of  the  history  of  painting 
was  designed  to  illustrate,  is  shown  to  be  true,  namely,  that 
the  rank  of  the  artist  depends  very  largely  indeed  upon 
the  advance  that  he  has  made  in  developing  the  possibili- 
ties of  color. 

This  advance  is  connected,  too,  with  a study  of  scien- 
tific principles.  There  are  infinite  diversities  of  shades 
and  tints  in  colors,  and  these  often  influence  and  entirely 
neutralize  one  another  when  brought  together  in  pig- 
ments. No  matter,  therefore,  how  much  taste  or  obser- 
vation an  artist  may  have  in  the  abstract,  these  cannot 
always  guide  him  to  successful  execution.  He  needs  the 
largest  aid  that  can  be  afforded  by  the  experience  and 
experiments  of  others.  This  fact  will  appear  more  clear, 
as,  taking  it  for  granted,  we  go  on  to  consider  the  subject 
as  it  will  be  unfolded  in  the  following  chapters. 


CHAPTER  XVIII. 


EFFECTS  OF  COLOR  AS  DISCOVERED  BY  SCIENTIFIC 
EXPERIMENTS. 

Newton’s  Discovery  of  the  Colors  of  the  Spectrum — They  are  Contained 
only  in  White  Light — The  Diversity  and  Brilliancy  of  the  Spectrum's 
Colors  Dependent  on  the  Amount  and  Intensity  of  the  Light — Bright- 
ness and  White  Making  all  Colors  Pale  ; Darkness  and  Black  Making 
them  the  Opposite — Names  of  the  Chief  Colors — The  Terms:  Flues, 
Full,  High,  Dark,  Light,  Pale,  Broken,  Shades,  Tints,  Tone,  Local, 
Positive,  Neutral,  Warm,  Cold,  Primary,  Secondary — Colors  Transmit 
and  Reflect  Rays  of  Like  Color  with  Themselves — Practical  Bearing  of 
this  upon  the  Kind  of  Light  with  which  Objects  are  Illumined,  Lamps, 
Sun,  etc. — Shows  why  Colors  are  Most  Vivid  when  Illumined  by  Light 
of  their  Own  Color — Why  White  Objects  Reflect  the  Color  Illumining 
them — What  are  the  Actual  Colors  of  Nature — Of  Foliage — Of  Water 
—Of  the  Atmosphere — Of  Objects  in  External  Nature  in  Light  or 
Shade,  when  the  Sun  is  on  the  Horizon — Especially  at  a Distance — 
When  the  Sun  is  in  the  Zenith — Colors  of  the  Same  Objects  in  Cloudy 
Weather  ; the  Terms  Cold  and  Warm — Effects  of  Light  and  Shade 
within  Doors— Cold  and  Warm  Colors  in  the  Representation  of  Dis- 
tance— These  Effects  Dependent  on  the  Degrees  of  Light — Difference 
of  Opinion  with  Reference  to  Certain  Deductions  Made  from  Acknow- 
ledged Facts  of  Aerial  Perspective — The  Apparent  Truth  with  Refer- 
ence to  the  Subject. 

JT  is  now  more  than  two  centuries  since  Newton,  analyz- 
ing the  rays  of  the  sun,  detected  that  all  the  different 
colors,  except  perhaps  extreme  purple,  are  contained  in 
light.  Most  of  us  know  how  to  reproduce  his  analysis. 
By  means  of  a mirror,  the  sun’s  rays  are  reflected  in  a 
small  band  through  a narrow  opening  in  a window-shade, 
or  blind,  and  sent  into  an  otherwise  darkened  room.  See 


309 


PROPORTION  AND  HARMONY. 


310 

Fig.  124.  When  they  enter  this  room  they  are  made  to 
pass  through  a glass  prism  the  edges  of  which  are  placed 
as  in  this  figure.  The  prism  turns  the  band  of  rays 
aside  from  its  direction,  and,  at  the  same  time,  separates 
it  into  an  infinitely  large  number  of  bands  of  rays  which 
are  colored,  and  each  of  which,  after  leaving  the  prism, 
continues  in  a straight  line.  If  these  bands  fall  on 
a white  wall  or  screen,  each  produces  a different  color, 


FIG.  124.— BREAKING  UP  A RAY  OF  WHITE  LIGHT. 

See  page  310. 


and  all  together  a series  of  colors  in  which  we  recognize  all 
that  are  in  the  rainbow.  Nearest  where  the  white  would 
have  fallen,  if  the  prism  had  not  intervened,  we  find  red, 
and  next  to  this  the  other  colors  in  this  order  : orange, 
yellow,  green,  blue,  indigo,  and  violet.  This  series  of 
colors  is  called  the  Spectrum. 

If  now,  in  the  white  on  which  we  see  the  spectrum,  we 
make  another  narrow  opening  parallel  to  the  one  made 
first,  and  back  of  this  receive  into  another  darkened  room, 
and  send  through  another  prism,  a ray,  red  or  green  or 
blue  as  the  case  may  be,  we  get,  as  a result,  no  further 


THE  SPECTRUM. 


311 

analysis  of  the  light.  The  red  or  green  or  blue  ray,  after 
passing  through  the  second  prism  still  remains  red  or  green 
or  blue.  The  conclusion  is  inevitable  that  it  is  only  com- 
pound light,  which,  when  analyzed,  can  be  separated  into 
the  different  colors. 

But  let  us  experiment  further  with  the  results  of  our 
analysis.  If,  by  bringing  our  curtains  near  the  prism,  we 
reduce  the  size  of  the  spectrum,  we  see  only  a few  of  the 
more  prominent  colors, — red,  green,  blue,  and  violet  per- 
haps. If  we  increase  its  size  we  find  orange  and  yellow 
between  the  red  and  green,  and,  in  these  as  well  as  in  all 
the  colors,  we  notice  an  incalculable  number  of  distinct 
varieties.  If  we  reduce  the  amount  or  brightness  of  the 
light  passing  through  the  prism,  the  colors,  one  after  an- 
other, become  more  and  more  dull  and  disappear.  Yellow 
and  orange  and  turquoise  blue  go  first,  leaving  a brown- 
ish red,  green,  and  violet ; then  the  red  and  violet  go,  and 
last  of  all  we  lose  sight  of  the  dull  green.  On  the 
contrary,  if  we  increase  the  amount  or  brightness  of  the 
light  analyzed,  all  the  colors  become  more  brilliant  and 
diversified. 

If  again,  turning  from  the  spectrum,  we  test  the  effects 
of  different  degrees  of  light  on  colored  pigments,  we  find 
that  in  a darkened  room,  a colored  surface,  say  of  blue, 
appears  to  be  dark  blue,  but  as  we  gradually  increase  the 
light  it  becomes  first  full  blue,  then  light  blue,  then  pale 
blue,  then,  in  light  of  great  intensity,  loses  its  blueness 
almost  entirely,  becoming  very  nearly  white.  So,  too,  if 
in  place  of  different  degrees  of  light,  we  use  black  or  white 
pigments,  mixing  them  with  colored  pigments,  we  find  the 
colors  becoming  respectively  darker  or  lighter.  To  make 
a practical  application  of  these  facts  before  we  leave  them, 
they  show  us  why  landscapes  representing  bright  sunshine 


312 


PROPORTION  AND  HARMONY. 


require  brilliant  and  diversified  tints  and  shades  of  all 
kinds,  whereas  those  representing  twilight  and  moonlight, 
which  are  only  diminished  sunlight,  require  an  absence 
of  all  brilliant  colors  and  often  of  anything  like  even  a 
decided  red,  yellow,  or  blue. 

From  what  has  been  said,  it  will  be  seen  that  the  dif- 
ferent kinds  and  degrees  of  colors  that  can  be  produced 
by  the  action  of  light  or  with  pigments  are  practically 
infinite.  At  the  same  time,  just  as  musicians  have  found 
it  convenient  to  select  a few  from  thousands  of  possible 
notes  and  name  them  A,  B,  C,  D,  etc.,  so  physicists  have 
agreed  upon  designating  certain  colors  by  the  following 
names  which,  with  the  definitions  of  some  other  terms, 
may  as  well  be  given  here.  The  names  of  the  colors  are 
taken  from  Von  Bezold’s  “Theory  of  Color.”  They  are 
Red  (Carmine,  Vermilion),  Orange,  Yellow,  Yellowish- 
green,  Green,  Bluish-green,  Turquoise-blue,  Ultramarine, 
and  Violet  (Bluish-violet,  Purplish-violet,  and  Purple). 

These  different  kinds  of  colors  are  termed  hues.  When 
hues  are  in  the  state  in  which  they  appear  in  the  spectrum, 
they  are  called  full  or  high  colors.  If  darker  than  in  the 
spectrum,  the  colors  are  termed  dark , if  lighter,  light ; if 
very  much  lighter,  pale  or,  what  means  the  same  thing, 
broken.  When  full  colors  are  made  darker,  their  different 
degrees  of  darkness  are  termed  shades.  When  they  are 
made  lighter  their  different  degrees  of  lightness  are  termed 
tints.  The  degree  of  coloring  or  of  dark  or  light  in  a 
shade  or  tint  determines  the  tone , as  when  we  speak  of 
a golden  and  gay,  or  a gray  and  sombre  tone.  Paintings, 
however,  are  not  generally  said  to  be  distinguished  by  tone 
except  when  pervaded  throughout  by  a similarity  of  tone. 
Local  color  is  a term  given  by  artists  to  what  appears  to 
them  to  be  the  inherent  hue  of  an  object  aside  from  any 


TERMS  APPLIED  TO  COLORS. 


313 


influence  upon  it  of  sunlight,  moonlight,  shade,  reflection, 
or  refraction.  However,  while  these  terms,  local  and  in- 
herent, are  thus  used,  it  must  be  borne  in  mind  that,  ac- 
cording to  physics,  the  colors  perceived  in  objects  do  not 
pertain  to  them  aside  from  effects  produced  in  connection 
with  them  by  the  vibratory  action  of  the  ether  waves. 
Some  bodies  have  such  a molecular  constitution  that  they 
absorb  certain  quantities  or  kinds  of  these  waves,  and 
reject  others.  A black  object  absorbs  nearly  all  of  them  ; 
a white  reflects  nearly  all  ; and  a gray  absorbs  some  and 
reflects  others.  These  three  differ  not  in  the  kinds  of 
waves  that  they  absorb  or  reflect,  but  in  their  quantities. 
Objects  that  have  what  we  term  color  differ  in  the  ways  in 
which  they  act  toward  different  kinds  of  waves,  rejecting 
or  reflecting  back  upon  the  ether  in  unequal  proportions 
certain  partial  constituents  of  the  waves,  which  they 
cannot  receive  because  these  do  not  accord  with  their  own 
natural  rate  of  oscillation  or  with  any  multiple  of  it. 

In  a positive  color  the  tint  or  shade  of  a single  hue  is 
prominent ; in  a neutral  color,  there  is  so  much  of  a 
mixture  that  there  is  no  predominating  hue.  The  warm 
colors,  so  called  for  reasons  to  be  given  hereafter,  are  the 
reds,  browns,  oranges,  yellows,  and  associated  colors  ; the 
cold  are  the  greens,  blues,  grays,  violets,  and  associated 
colors.  Primary  is  a term  formerly  applied  to  red,  yellow, 
and  blue  because  they  were  supposed  to  be  primitives  from 
which  the  secondary  colors,  orange,  green,  and  violet,  were 
derived,  orange  by  mixing  red  and  yellow,  green  by 
mixing  yellow  and  blue,  and  violet  by  mixing  blue  and 
red.  For  reasons  to  be  given  by-and-by,  however,  these 
distinctions  between  primary  and  secondary  are  not  now 
considered  tenable. 

Now  let  us  return  to  the  spectrum  on  the  curtain.  If 


3H 


PROPORTION  AND  HARMONY. 


we  take  a piece  of  colored  glass — say  red  flashed  glass 
colored  with  protoxide  of  copper — and  hold  it  before  the 
opening  made  for  the  light  in  the  window,  so  as  to  allow 
only  red  rays  to  enter  the  room  and  pass  through  the 
prism  ; or  if  we  hold  the  red  glass  between  the  prism  and 
the  spectrum  ; or  if  we  hold  the  red  glass  to  our  eyes  and 
look  through  it  at  the  spectrum  ; — in  all  these  cases  we  find 
that  all  the  rays  passing  through  the  red  glass,  either  be- 
tween the  sunlight  and  the  spectrum,  or  between  the  spec- 
trum and  our  eyes,  is  red,  or,  owing  to  a slight  imperfection 
in  all  colored  glass,  orange,  which  is  nearly  related  to  red. 
We  notice,  too,  that  the  red  and  orange  are  situated  in  the 
spectrum  on  the  screen  just  where  they  were  when  the 
other  colors  were  visible,  which  other  colors  are  now 
obliterated.  We  may  continue  in  the  line  of  these 
experiments  by  painting  screens  in  many  different  colors 
and  sending  white  light  through  the  prism  on  to  them. 
In  such  cases  we  shall  find  invariably  that  the  spectrum 
which  would  have  been  produced  on  a white  screen  is 
represented  by  only  certain  colors  allied  to  those  in  which 
the  screen  is  painted,  which  colors  appear  in  the  same 
relative  places  on  the  painted  screen  in  which  they  would 
have  appeared  on  the  white  screen.  Those  who  have  read 
thus  far  this  series  of  volumes,  or  even  the  first  part  of 
the  present  volume,  will  be  interested  in  noticing  how  this 
natural  tendency  of  color  to  transmit  or  reflect  rays  that 
are  like  its  own  accords  with  the  artistic  tendency  in  the 
direction  of  unity,  and  of  grouping  like  with  like,  from 
which,  as  shown  by  the  chart  on  page  3,  all  the  methods 
of  art  composition  are  developed. 

Now  let  us  notice  the  bearings  of  the  facts  just  stated 
upon  the  effects  and  therefore  upon  the  methods  of  repre- 
senting light  and  shade.  We  may  begin  by  observing  that 


COLORED  LIGHT  AS  AFFECTING  COLORS.  3 1 5 


we  see,  from  what  has  been  said,  why  it  is  that  colored 
objects  appear  black,  if  illumined  only  by  a color  which 
they  do  not  possess.  Little  blue  and  violet  are  present 
in  the  light  of  lamps  and  candles.  Therefore,  in  the  night- 
time, while  red  and  yellow  colors  in  dresses,  paintings, 
and  decorations  can  generally  be  seen  with  their  full  ef- 
fects, blue,  if  allied  to  green,  appears  like  green,  and  if 
allied  to  violet,  like  black  ; and  violet,  if  allied  to  blue, 
like  gray,  and  if  allied  to  red,  like  reddish-brown.  Some 
years  ago,  an  “ Academy  of  Music  ” in  one  of  our  principal 
cities  was  refitted  and  papered  in  blue.  The  effect,  on 
the  opening  night,  was  so  gloomy  and  disagreeable  that, 
before  a second  performance,  the  entire  interior  was  re- 
papered in  a warmer  color.  In  cases  where  it  is  desira- 
ble to  know  by  daylight  how  decorations  or  paintings  will 
appear  by  candle-light,  a reasonably  trustworthy  opinion 
of  this  may  be  gained  by  looking  at  them  through  an 
orange-  or  yellow-tinted  glass.1 

The  facts  that  we  are  considering  show  us  again  why 
colored  objects  appear  most  vivid  when  illumined  by  light 
of  their  own  color.  The  reason  is  that,  under  such  condi- 
tions, they  transmit  or  reflect  all  the  light  illumining  them, 
none  of  which  is  lost.  In  this  way,  all  colors  act  like 


1 The  following  tables  will  be  of  interest  here.  They  are  the  results  of 
experiments  published  by  Prof.  O.  N.  Rood,  in  his  “ Modern  Chromatics,” 
chap,  xi.,  pp.  152-154. 


yellow  LIGHT  falling  on  paper  painted  with 


Carmine  gave Red-orange. 

Vermilion Bright  orange-red. 

Orange Bright  orange-yel- 

low. 

Chrome-yellow Bright  yellow. 

Gamboge Bright  yellow. 

Yellowish-green Yellow. 

Green Bright  yellow- 

green. 


Blue-green  gave Yellow-gre  en 

(whitish). 

Cyan-blue Y ellow-green . 

Prussian-blue Bright  green. 

Ultramarine-blue White. 

Violet Pale  reddish  tint. 

Purple-violet Orange  (whitish). 

Purple Orange. 

Black Yellow. 


3 16 


PROPORTION  AND  HARMONY. 


white  toward  light  of  their  own  color.  Red  figures  on  a 
white  ground,  for  instance,  disappear  in  red  light.  For 
the  same  reason,  colors  are  always  more  dark,  when  inside 
of  a fold  of  drapery,  or  of  a niche,  or  in  the  corner  of  a 
room,  especially  where  there  is  gilding. 

The  same  facts  explain,  too,  why  white  objects  reflect 
often  the  color  illumining  them.  A white  wall,  for  instance, 
appears  white  by  daylight,  and  red  by  firelight.  Of  course 
the  reason  of  this  is  that  white  contains  all  the  colors,  and 

red  LIGHT  falling  on  paper  painted  with 


Carmine  gave. . . . 

Red. 

Blue-green  gave 

Vermilion 

Cyan-blue 

Orange 

scarlet. 

Prussian-blue 

...Re  d-p  u r p 1 e or 
blue-violet. 

Chrome-yellow  . . 

Violet 

Gamboge 

Purple- violet 

Yellowish-green  . 

Purple 

Green 

(whitish). 

Black  

GREEN  LIGHT  falling 

on  paper  painted  with 

Carmine  gave. . . . 

Prusssian-blue  gave. 

Vermilion 

blue. 

greenish-yellow. 

Ultramarine-blue  . . . . 

Orange 

ish-yellow. 

Violet 

violet-blue  (all 

Chrome-yellow. . 

whitish). 

Gamboge 

Purple-violet 

Yellowish-green. . 

pale  blue. 

Green 

Purple 

Blue-green 

gray,  reddish- 

Cyan-blue 

Black 

gray. 

BLUE  LIGHT  falling 

on  paper  painted  w 

ith 

Carmine  gave  . . 

Purple. 

Blue-green  gave  .... 

Vermilion 

Cyan-blue 

....Blue. 

Orange 

Prussian-blue 

. . . . Blue. 

Chrome-yellow. . 

Ultramarine-blue . . . 

Blue. 

greenish-gray. 

Violet 

Gamboge 

let-blue. 

greenish-gray. 

Purple-violet 

Yellowish-green . 

Purple 

Green 

ple-violet. 

blue. 

Black 

REAL  COLORS  OF  NATURAL  OBJECTS.  3 1 7 

so  is  prepared  in  each  case  to  give  back  the  color  that  it 
receives. 

Once  more,  these  same  facts  show  us  how  to  find  out 
what  the  colors  of  objects  actually  are.  The  results  of 
using  colored  glasses  in  connection  with  spectrums,  as  ex- 
plained on  page  314,  and  of  sending  white  light  through  a 
prism  upon  a colored  screen,  must  follow  if  applied  to  an 
object  of  any  color.  If  so,  the  use  of  colored  glasses  and 
spectrums  must  enable  us  to  detect  everywhere  in  the  ap- 
pearances of  nature,  the  presence  of  color  which  otherwise 
we  might  not  see.  The  connection  is  apparent  between  a 
knowledge  of  the  discoveries  thus  made,  and  the  success- 
ful representation  of  many  of  the  appearances  both  of 
texture  and  of  life.  Especially  is  it  important  to  notice 
what  has  been  found  out  in  this  way  with  reference  to  the 
colors  actually  visible  in  the  foliage,  water,  and  atmos- 
phere about  us,  as  perceived  under  different  conditions  of 
light  and  shade,  by  day  and  by  night. 

With  reference  to  the  first  of  these,  namely,  foliage,  it 
has  been  observed  that  a spectrum,  which,  when  thrown 
upon  green  pigment,  shows  only  a green  color,  if  thrown 
upon  the  green  of  foliage  shows  tints  both  of  red  and 
yellow.  Or  if  the  trees  be  examined  through  a red  glass, 
it  has  been  observed  that  in  the  degree  in  which  the  glass 
transmits  only  the  red  rays  the  leaves  are  red,  although 
the  blue  sky  above  them,  as  also  green  fabrics  and  pig- 
ments about  them,  appear  black.  The  conclusion  is  in- 
evitable that  the  coloring  matter  of  foliage,  which  is  called 
chlorophyl,  contains,  besides  green,  other  and  warmer 
colors.  Of  course,  for  one  who  knows  this,  the  suggestion 
of  the  tints  of  red  and  yellow,  in  the  green  about  him, 
will  greatly  augment  his  interest  in  natural  scenery.  Nor 
does  it  require  more  than  a slight  degree  of  effort  to  en- 


3 1 8 PROPORTION  AND  HARMONY 

able  him  actually  to  perceive  these.  In  coloring,  as  in 
everything,  men  come  to  see  what  they  try  to  see.  What 
but  persistence  in  scrutinizing  and  criticising  their  neigh- 
bors’ attire  makes  the  color-sense  in  women  so  much 
stronger  than  in  men?  As  shown  in  Chapters  XII.  to 
XIV.  of  “ Art  in  Theory,”  beauty,  even  as  recognized  by 
the  senses,  depends  largely  upon  effects  produced  upon 
the  mind.  The  truth  underlying  such  injunctions  as 
“ Seek  ye  first  the  kingdom,”  “ The  kingdom  is  within 
you,”  and  “ Except  a man  be  born  from  above  he  cannot 
see  the  kingdom,”  is  of  universal  applicability.  Those 
who  strive  to  enter  into  the  realm  of  coloring  will  find 
capabilities  within  themselves  which,  if  properly  used, 
will  introduce  into  their  field  of  vision  an  infinite  variety 
of  tints  and  shades  which,  so  far  as  concerns  the  effect 
upon  the  senses,  transcend  in  beauty  those  which  the  ordi- 
nary man  perceives,  in  a degree  akin  to  that  in  which  the 
new  earth  pictured  in  the  Apocalypse  transcends  the  old 
earth  of  ordinary  experience.  It  is  only  the  man,  too, 
who  is  able  to  perceive  these  colors  in  nature,  by  whom 
they  can  be  fully  recognized  as  representing  truth  when 
they  are  placed  upon  the  canvas  of  the  painter.  Yet 
here  they  are  essential.  That  indescribable  effect  of  vi- 
tality which  characterizes  the  grasses  and  grains  of  some 
landscapes  is  owing  largely  to  the  presence  in  them  of 
these  red  and  yellow  tints.  It  is  these  that  make  of  the 
dead  green  a “ living  green,”  just  as  surely  as  the  same 
tints,  were  they  used,  would  give  to  the  picture  of  a corpse 
the  glow  and  warmth  of  life. 

Experiment  has  found  also  that  water  has  a color  of  its 
own,  which  is  blue.  But,  besides  this,  it  may  transmit 
the  color  of  whatever  material  happens  to  be  beneath  it, 
and  may  reflect  from  its  surface  the  color  of  a blue  or  of  a 


COLORS  IN  THE  MORNING  AND  AT  NOON.  319 


gray  sky,  or  of  anything  that  happens  to  be  above  it.  Di- 
rect rays,  too,  falling  upon  it  from  the  sun,  or  moon,  or 
any  like  source  of  light,  are  polarized. 

The  atmosphere,  which  probably  contains  water  in  the 
form  of  minute  bubbles,  has  a whitish-blue  tint  when  the 
light  falls  upon  it  as  it  falls  upon  the  horizon  at  noon  or 
on  the  space  intervening  between  us  and  distant  moun- 
tains. But  the  same  atmosphere  has  a reddish  and  yel- 
lowish tint  when  the  light  is  transmitted  through  it  like 
the  rays  of  the  sun  or  moon  if  near  the  horizon. 

Returning  now,  more  particularly,  to  light  and  shade , 
which,  in  every  case,  are  necessarily  modified  by  the  par- 
ticular colors  of  the  object  which  transmits  or  reflects 
them,  we  may  notice,  first,  how  what  has  been  said  with 
reference  to  the  coloring  of  foliage  explains  the  great  dif- 
ferences between  the  trees  of  a landscape  when  illumined 
and  when  in  shadow,  as  well  as  the  differences  in  color  in 
both  their  illumined  and  their  shaded  parts  if  lighted  by 
a sun  near  the  horizon,  or  by  one  near  the  zenith.  In 
the  morning  or  evening  the  direct  rays  coming  from  the 
sun  to  the  object  and  from  the  object  to  the  eye  make  a 
long  passage  through  the  atmosphere,  and  this,  because 
the  light  is  thus  transmitted  through  it,  has,  as  has  been 
said,  a reddish  or  yellowish  tint.  Possibly,  too,  the  fact 
that  this  atmosphere  lies  close  against  the  warm  colors 
of  the  ground  may  influence  its  own  color  to  some  extent. 
At  any  rate,  the  sunlight  at  this  time  gives  to  foliage  and 
other  objects  the  red  and  yellow  tints  that  are  in  the  me- 
dium through  which  it  passes.  Objects  in  shadow,  how- 
ever, that  are  not  lighted  up  by  these  direct  rays  of  the 
sun  are  illumined  mainly  by  the  reflected  blue  and  gray 
light  of  the  sky.  They  therefore  show  cold  tints. 

This  principle,  as  will  be  noticed,  though  applying  to 


320 


PROPORTION  AND  HARMONY. 


some  extent  to  all  objects  at  sunrise  and  sunset,  applies 
especially  to  those  at  a distance,  the  rays  from  which 
must  make  a long  passage  through  the  lower  atmosphere. 
Therefore  it  is  exemplified  particularly  in  the  colors  of 
mountains  and  clouds  on  the  horizon.  The  white  snows 
of  Mt.  Blanc  at  sunrise  are  often  as  ruddy  with  reflected 
light  on  one  side  of  the  horizon  as  are  the  clouds  immedi- 
ately above  the  sun  on  the  other.  The  green  leaves  of 
midsummer  upon  a mountainside  are  sometimes  tinged 
at  sunset  with  a color  as  brilliant  as  was  ever  seen  in  the 
full  glory  of  autumn. 

So  much  with  reference  to  objects  illumined  or  in 
shadow,  when  the  sun  is  near  the  horizon.  As  this  ap- 
proaches the  zenith,  however,  these  conditions  are  reversed, 
and  so  are  the  colors.  Then  the  light  of  the  sun  is  rein- 
forced on  every  side  by  the  reflected  cold  colors  of  the 
sky.  For  this  reason  objects  in  sunshine  at  this  time 
show  bluish  and  cold  tints  ; while  those  in  shadow  show 
the  opposite,  either  by  way  of  contrast,  or  because  all 
the  light  illumining  them  is  reflected  from  the  warm 
colors  of  the  ground. 

In  cloudy  weather,  the  sun  is  obscured,  and  the  light 
that  we  have  is  reflected  from  the  cold  blue  or  gray  tints 
of  the  clouds.  Nor  are  there  any  decided  shadows  on 
the  earth.  Accordingly,  as  we  look  off  over  it,  all  the 
tints  partake  of  the  character  of  those  in  the  sky.  Cloudy 
days  are  usually  cold.  It  is  for  this  reason,  probably, 
that  the  tints  and  shades  usually  prevailing  then  are 
termed  cold;  whereas  the  yellows  and  reds  which  we  asso- 
ciate with  sunlight  and  firelight  are  termed  warm. 

Within  doors,  all  direct  illumining  usually  comes  from 
the  blue  light  of  the  sky.  Therefore  cold  tints  are  seen 
wherever  there  is  superficial  reflection  on  the  face  or  hair 


AERIAL  PERSPECTIVE. 


321 


Or  drapery.  For  this  reason,  warm  colors  in  interiors 
produce  more  agreeable  effects  than  their  opposites,  not 
only  because  they  light  up  better  at  night,  as  shown  on 
page  315,  but  because  they  counteract  the  effects  of  the 
cold  tints  that  appear  by  day. 

There  is  one  other  important  application  of  the  dis- 
tinction made  a moment  ago  between  the  warm  and  cold 
colors.  It  arises  in  connection  with  the  representation 
of  distance  or  of  aerial  perspective.  As  stated  in  Chapter 
XVI.  of  “ Painting,  Sculpture,  and  Architecture  as  Repre- 
sentative Arts,”  the  general  principle  underlying  this  is 
that,  as  objects  recede  in  the  distance,  they  grow  more  dull 
in  color,  and,  in  the  extreme  distance,  change  their  color, 
passing  from  one  containing  more  light  into  one  con- 
taining less  light,  bright  red,  for  instance,  passing  into 
darker  red  ; orange  into  red-orange;  and  yellow  into  yel- 
lowish-orange ; green  into  bluish-green  ; and  blue  into 
darker  blue,  and  bluish-purple.  In  Prof.  O.  N.  Rood’s 
“Modern  Chromatics,”  chap,  xvi.,  p.  274,  will  be  found 
the  following  table  of  small  intervals,  showing  the  influence 
upon  the  colors  mentioned  of  a greater  and  lesser  degree 
of  luminosity. 


TABLE  OF  SMALL  INTERVALS. 


Lighter . 

Darker. 

Ligkter. 

Darker. 

Orange-red 

Red. 

Green 

Orange 

Cyan-blue 

Orange-yellow 

Blue 

Yellow 

Purple 

Greenish-yellow 

Y ello  wish-green 

Red 

These  changes  in  colors  take  place  in  the  distance  be- 
cause less  light  falls  upon  the  objects  there,  and  more 
atmosphere.  In  the  degree  in  which  less  light  falls  upon 
them,  we  have  found  (see  page  31 1)  that  bright  colors, 


PROPORTION  AND  HARMONY. 


especially  the  warm  reds,  oranges,  and  yellows— and  the 
same  thing  is  true  also  of  blues — disappear.  We  have 
found,  too,  that  in  certain  cases  in  the  degree  in  which 
more  atmosphere  intervenes  between  us  and  these  objects, 
as,  for  instance,  when  we  are  looking  at  mountains  and 
trees  under  a sun  high  in  the  heavens,  they  exhibit  blue, 
gray,  or  violet  tints. 

The  statements  made  with  reference  to  this  subject 
thus  far,  few  will  dispute.  Though  some  otherwise  good 
artists  like  Cabanel,  Bouguereau,  and  Gdrome,  seem  at 
times  to  ignore  the  truth  that  they  contain,  the  great 
majority  of  modern  painters,  men  like  Daubigny,  Troyon, 
Lepine,  Jules  Breton,  Millet,  Corot,  Lerolle,  Frere,  Israels, 
Decamps,  Fromentin,  De  Nittis,  and  Inness,  exemplify 
it.  There  is  much  difference  of  opinion,  however,  with 
reference  to  some  of  the  deductions  that  are  drawn  from 
the  acknowledged  principles  of  “ aerial  perspective.”  It 
seems  to  follow  from  the  facts  instanced  in  the  last 
paragraph,  that  if  we  see  very  bright  warm  colors  associ- 
ated with  cold  ones,  we  naturally  judge  that  the  warm  are 
the  nearer  us.  The  correctness  of  this  inference  seems  to 
be  confirmed  by  an  argument  to  the  effect  that  the  warm 
colors,  being  formed  by  waves  of  greater  length  than  the 
cold,  are  more  exciting  to  the  optic  nerve  and  therefore 
attract  more  of  its  attention.  To  this,  a subjective  con- 
sideration is  added,  by  Von  Bezold  in  his  “ Theory  of 
Color.”  He  says  that  the  warm  colors,  especially  red,  are 
at  the  least  refrangible  end  of  the  spectrum.  The  rays 
producing  red,  therefore,  pass  through  the  prism  and  on- 
ward very  nearly  in  a straight  line,  whereas  the  opposite 
is  the  case  with  those  producing  cold  colors.  By  conse- 
quence, we  cannot  at  the  same  time  see  clearly  the  colors 
at  both  ends  of  the  spectrum.  We  must  place  them  at 


AERIAL  PERSPECTIVE. 


323 


different  distances,  or  vary  the  accommodation  of  the  eye. 
If  they  are  at  the  same  distance,  in  looking  first  at  red, 
say,  and  then  at  blue,  we  necessarily  lessen  the  curvature 
of  the  lens  by  means  of  a muscle  in  the  eye.  (See  Fig. 
1 14,  page  273.)  That  is  to  say,  we  do  the  same  that  we 
should  do  did  blue  belong  to  a more  remote  object. 
What  more  natural,  then,  than  that  it  should  appear  to  be 
more  remote  ? Such  facts  show  the  basis  and  explanation 
of  the  theory  that  in  painting,  other  things  being  equal, 
the  warm  colors  cause  objects  depicted  through  the  use  of 
them  to  seem  to  be  in  the  foreground,  while  the  cold  colors 
cause  them  to  seem  to  be  in  the  background.  Painters  tell 
us  that  it  is  therefore  important  in  pictures  of  the  silhouette 
style  to  use  a warm  color  on  a cold  ground,  and  not  the  oppo- 
site. Decorators,  too,  recognize  that  warm  colors  used  on 
walls  and  ceilings  make  rooms  seem  smaller  or  more  cozy, 
while  cold  colors  make  them  seem  larger.  A gentleman 
with  whom  the  author  is  acquainted,  in  approaching  in  his 
company  a row  of  houses  all  of  which  were  colored  gray 
except  one,  which  was  yellow,  asked  why  the  yellow  house 
was  not  built  back  on  a line  with  the  others.  He  could 
not  believe  that  it  did  not  project  in  front  of  them. 
Ruskin,  indeed,  in  his  “ Elements  of  Drawing,”  declares 
that  this  idea  with  reference  to  the  effects  of  the  warm  and 
cold  colors  is  erroneous,  that  it  is  their  quality  (as  depth, 
delicacy,  etc.)  which  expresses  distance,  not  their  tint ; 
while,  on  the  other  hand,  Von  Bezold  in  his  “Theory  of 
Color  ” says  that  when  the  brightness  of  the  colors  is  not 
approximately  equal,  the  bright  colors  advance  and  the 
dark  retire.  But  there  is  nothing  irreconcilable  in  these 
statements,  nor  between  them  and  what  has  been  said 
here,  or  was  said  in  Chapter  XVI.  of  “ Painting,  Sculpture, 
and  Architecture  as  Representative  Arts.”  As  a rule, 


324 


PROPORTION  AND  HARMONY. 


warm  colors  appear  where  there  is  the  most  light,  as  in 
brilliant  sunshine;  and,  whatever  colors  appear,  the  nearer 
they  are,  the  greater  usually  is  the  light  illumining  them. 
Both  principles  undoubtedly  have  an  influence  in  effects 
of  aerial  perspective.  But  besides  this,  it  must  be  borne 
in  mind  that  effects  of  color  cannot  entirely  overbalance 
those  of  outline.  A warm  hue  on  a distant  cloud  in  a 
representation  of  sunset,  would  not  necessarily  seem 
nearer  than  a gray  hue  on  a cloud  quite  near  us.  In 
Titian’s  “ Scourging  of  Christ  ” a soldier  shown  by  the 
drawing  to  be  in  the  extreme  foreground  does  not,  because 
he  wears  gray  armor,  seem  farther  off  than  the  Christ  who 
is  clothed  in  red,  yet,  by  the  drawing,  is  shown  to  be  a 
little  back  of  the  foreground.  But  the  soldier,  on  account 
of  the  color  of  his  armor,  is  not  the  foremost  object  thrust 
upon  attention,  and  it  was  undoubtedly  to  prevent  his 
appearing  to  be  this  that  the  painter  represented  him  in 
gray. 


CHAPTER  XIX. 


BASIS  OF  COLOR-HARMONY. 

The  Tendency  in  Natural  Color  for  Like  to  Go  with  Like  in  Analogy  with 
the  Same  Tendency  in  Natural  Language — Differences  of  Opinion 
Regarding  the  Essential  Requirements  of  Color-Harmony — Some  Truth 
in  All  these  Opinions,  but  only  so  far  as  Certain  Principles  are  Fulfilled — 
Those  of  Unity,  Variety,  Complexity,  Order,  Confusion,  Counteraction, 
Grouping — Like  with  Like  in  the  Colors  of  Nature,  is  the  Basis  for 
the  Same  Arrangement  by  Way  of  Comparison  and  Contrast — Colors 
Called  the  Contrasting  or  Complementary  Colors  not  All  that  really 
Contrast — The  Complementary  Colors — What  they  are  as  Determined 
by  Dividing  the  Rays  of  Light — As  formerly  Determined  by  Mixing 
Pigments — Proof  of  the  Erroneousness  of  the  Latter  Method — Von 
Bezold’s  Color  Chart — As  One  Complementary  Becomes  Brighter,  the 
Other  Becomes  Darker — -Wide  Differences  in  the  Complementaries  of 
Different  Shades  of  Green. 

TT  was  shown  in  Chapter  XVIII.  that  objects  in  nature 
having  what  the  artist,  but  not  the  physicist,  terms 
inherent  or  local  colors,  acquire,  when  arranged  together, 
as  in  a landscape,  shades  and  tints  from  one  another; 
and  this  tendency  is  sometimes  exemplified  so  emphatic- 
ally that  in  certain  cases  almost  every  appearance  seems 
subordinated  to  the  influence  of  one  dominating  hue. 
This  natural  tendency  of  color  seems  to  prepare  it,  at 
least,  to  accord,  as  already  intimated,  with  the  artistic 
tendency  in  the  direction  of  unity  and  of  grouping  like 
with  like  from  which,  as  shown  in  the  chart  on  page  3, 
all  the  methods  of  art-composition  are  developed.  In 
Chapter  VII.  of  “ Rhythm  and  Harmony  in  Poetry  and 


325 


326 


PROPORTION  AND  HARMONY. 


Music  ” it  was  shown  that  a similar  tendency  in  the  use 
of  natural  language  underlies  many  of  its  artistic  develop- 
ments. Each  syllable  has  its  inherent  or  local  sound,  and 
yet,  when  used  with  other  syllables,  as  exemplified  in  the 
cries  of  street-venders,  and  in  popular  maxims  and  mottoes, 
an  instinctive  physical  prompting  connected  with  ease  in 
utterance  causes  men  to  choose  and  arrange  words  so 
that  like  sounds  shall  go  with  like ; and  it  is  this  fact 
with  reference  to  natural  expression  that  finally  leads  to 
the  use  of  such  methods  as  alliteration,  assonance,  rhyme, 
phonetic  syzygy,  and  gradation,  characterizing  poetic 
harmony.  So  the  fact  just  mentioned  in  connection  with 
color — a fact  which  even  an  artist  who  did  not  know  it 
would  exemplify  when  giving  merely  natural  expression 
to  his  desire  to  imitate  nature — leads,  when  artistically 
developed,  to  many  of  the  most  important  effects  charac- 
terizing color-harmony. 

With  reference  to  the  essential  requirements  of  this 
harmony,  there  have  been  many  different  opinions.  Some 
of  the  early  Italians  based  it  upon  the  presence  of  what 
were  formerly  termed  the  three  primary  colors,  namely, 
red,  yellow,  and  blue,  or  else  of  the  three  secondary  colors, 
namely,  orange,  green,  and  purple;  and  in  every  painting, 
irrespective  of  its  subject,  they  thought  it  imperative  to 
introduce  all  three  of  one  of  these  sets.  Since  then, 
others  have  supposed  harmony  to  depend  upon  a com- 
bination of  two  complementary  colors,  which  two,  accord- 
ing to  opinions  formerly  held,  were  either  red  and  green, 
yellow  and  purple,  or  blue  and  orange.  (See  page  332.) 
In  addition,  moreover,  to  the  question  of  the  colors  them- 
selves, it  has  been  discussed  whether  either  the  three,  or 
the  two  thus  deemed  to  be  essential,  should  be  dis- 
tributed in  approximately  equal  or  unequal  quantities. 


BASIS  OF  COLOR-HARMONY. 


327 


Again,  with  a slight  modification  of  the  preceding  theories, 
harmony  has  been  based  upon  a greater  proportionment 
of  warm  than  cold  colors  ; and  finally  it  has  been  claimed 
that  it  consists  mainly  in  arranging  like  colors  together, 
varied  mainly  by  minute  gradations  (see  page  409)  and 
producing  thus  the  effect  which  is  sometimes,  by  way  of 
distinction,  termed  tone.  (See  page  355.) 

Of  course  there  must  be  some  truth  underneath  each 
of  these  theories,  or  it  would  find  fewer  advocates.  If 
so,  there  ought  to  be  some  general  principle  equally 
applicable  to  them  all.  But  what  this  principle  is,  does 
not  appear  upon  the  surface.  Possibly,  however,  it  may 
be  made  to  appear,  in  case  we  can  look  deep  enough  into 
the  subject.  In  trying  to  do  this,  as  the  subject  is  the 
artistic  harmony  of  color,  there  is  no  better  course  to 
pursue  than  to  go  back  and  trace  from  their  beginnings 
the  successive  art-methods  through  which,  as  indicated 
in  the  chart  on  page  3,  harmony  has  been  developed.  In 
carrying  out  this  plan,  notice,  first,  the  relationship  be- 
tween the  conditions  of  colors  as  they  appear  in  nature 
and  the  possibility,  in  depicting  them,  of  securing  the 
general  effect  of  unity  by  carrying  out  the  fundamental 
art-principle  of  putting  like  with  like.  Whatever  is  copied 
from  nature  manifests,  as  a rule,  much  likeness  of  hue. 
Even  when  the  foliage  is  not  all  green,  or  the  sky  all 
blue,  or  the  rocks  all  brown,  or  the  birds  or  beasts  which 
one  finds  in  the  same  group  all  of  one  shade,  the  very 
light  with  which  they  are  illumined  has  a tendency  to 
develop,  as  we  found  on  pages  314  to  317,  a sameness  in 
them. 

At  the  same  time,  the  natural  forms  which  furnish  the 
painter  with  his  subjects  are  never  absolutely  uniform  in 
color,  and  although  some  peculiar  condition  of  scene,  as 


328 


PROPORTION  AND  HARMONY. 


on  a desert  or  a sea;  or  of  light,  as  in  a storm  or  at  sun 
set,  may  give  an  objective  tinity  of  appearance,  and,  very 
likely,  for  reasons  that  physiology  has  not  yet  fully  dis- 
covered, a subjective  unity  of  effect  upon  the  retina 
(see  page  347),  this  unity  must  include  much  variety , and, 
therefore  complexity  both  of  inherent  hues  and  of  these 
as  modified  by  the  never  failing  influence  of  light  and 
shade  and  distance.  Owing  to  these  facts,  it  is  evident 
that  the  artist  cannot,  in  many  cases,  secure  the  unity 
of  effect  which  he  desires  without  very  consciously  avail- 
ing himself  of  his  possibilities  by  selecting  for  presentation 
objects  of  such  hues,  and  arranging  them  with  reference 
to  their  color-influence  upon  one  another  in  such  an  order, 
as  to  avoid  confusion,  or,  as  one  would  say,  to  counteract 
this  by  means  of  th z grouping.  See  page  3. 

The  fundamental  method  of  putting  like  with  like  and 
thus  securing  effects  of  unity  through  order,  is,  as  we  have 
found,  comparison.  But  comparison,  as  we  have  also 
found  (see  page  3),  can  never  apply  to  all  the  appearances 
brought  together  in  an  art-form.  Some  of  these  must  con- 
trast. Contrast,  as  an  art-method,  has  the  effect  of  empha- 
sizing one  form  or  color — whichever  it  may  be — by  placing 
it  in  juxtaposition  to  some  contrary  form  or  color.  Thus 
the  differences  between  the  two  are  made  to  seem  greater 
than  they  really  are.  The  impressiveness  of  the  tragedy  in 
Shakespeare’s  plays  is  often  much  enhanced  by  being 
presented  side  by  side  with  comedy.  (See  Chapter  II.  of 
“The  Genesis  of  Art-Form.”)  Perfectly  harmonic  chords  in 
music  often  seem  much  sweeter  by  being  made  suddenly 
to  follow  an  abrupt  transition  through  a series  of  un- 
resolved sevenths.  (See  Chapter  XV.  of  “ Rhythm  and 
Harmony  in  Poetry  and  Music.”)  So  in  painting,  two 
colors  in  juxtaposition  have  their  peculiarities  particularly 


THE  COMPLEMENTARY  COLORS.  329 

emphasized.  An  object  slightly  darker  than  a surface 
upon  which  it  is  placed  appears  to  be  very  much  darker 
than  it,  or,  if  slightly  lighter,  very  much  lighter.  This  is 
a principle  that  applies  to  crayon  as  well  as  to  color. 
See  the  upper  right  picture  in  Fig.  102,  page  235.  There 
is  a contrast  between  mere  light  and  shade ; and  the 
term  used  in  the  general  way  thus  indicated  may  apply 
to  the  juxtaposition  of  any  colors  that  are  not  the  same. 

But  in  painting  the  term  has  come  to  have  a specific 
meaning, — a meaning  more  appropriately  expressed,  hotv- 
ever,  by  another  word,  which  is  used  interchangeably 
with  it,  complementary.  Certain  colors,  when  brought 
together,  have  the  effect  of  greatly  enhancing  one  another’s 
brilliancy.  Because  they  differ,  they  are  called  contrast- 
ing colors  ; because  they  differ  in  a particularly  effective 
way,  they  are  called  the  contrasting  colors.  But  experi- 
ments conducted  according  to  various  methods,  some  of 
which  will  soon  be  described,  have  proved  that,  while 
these  colors  contrast , there  is  a sense  in  which  they  are 
fitted  to  go  together,  in  fact  are  allied,  and  thus  manifest 
the  influence  of  contrast  as  counteracted  by  that  of  coin- 
parison.  They  do  this,  moreover,  in  accordance  with  a 
law  which  is  exemplified  in  every  department  of  art, 
whenever  comparison  and  contrast  are  both  present  and 
yet  are  joined  by  way  of  complement.  See  page  3,  also 
Chapter  III.  of  “The  Genesis  of  Art-Form.” 

In  order  to  recognize  how  these  colors  popularly  called 
the  contrasting  ones  are  in  a true  and  scientific  sense  com- 
plementary, let  us  go  back  to  an  examination  of  the  results 
of  experiments  with  the  spectrum.  On  page  310,  it  was 
shown  that  white  light,  i.  e.,  ordinary  sunlight,  produces, 
when  analyzed,  all  the  different  colors ; from  which  fact  it 
was  said  that  the  conclusion  is  drawn  that  the  different 


330 


PROPORTION'  AND  HARMONY. 


colors  combined  produce  white  light.  Many  experiments 
have  served  to  confirm  this  conclusion.  If,  for  instance, 
by  means  of  an  apparatus  made  for  the  purpose,  the 
prism  causing  a spectrum  be  made  to  revolve  rapidly,  a 
white  round  image  will  take  the  place  of  the  spectrum  on 


FIG.  125.— FORMATION  OF  COMPLEMENTARY  COLORS. 

See  page  331. 


the  wall.  If  a color  top,  on  a disk  of  which  all  the  colors 
are  represented,  be  spun  rapidly,  a grayish-white  appears 
where  the  colors  are.  But  if  all  the  colors  together  make 
white,  it  follows  that  the  absence  from  white  light  of  any  of 
its  constituent  elements  must  produce  a color.  This  logical 
inference  has  been  confirmed  by  the  following  among  other 
experiments.  Between  the  prism  and  the  spectrum  cast 


THE  COMPLEMENTARY  COLORS. 


331 


by  it,  according  to  the  explanations  given  on  page  310, 
a lens  bounded  by  cylindrical  surfaces  is  introduced.  See 
Fig.  125,  page  330,  and  C in  Fig.  126.  This  lens  is  so 
constructed  that  it  reunites  the  prismatic  bundle  of  rays 
into  a single  band,  i.  e.,  it  restores  these  rays  to  the 
same  condition  in  which  they  were  before  they  reached 
the  prism  from  the  slit  in  the  window.  This  cylindrical 
lens  now  gathers  the  rays  together,  and  casts  upon  the 
wall,  where  the  spectrum  was  before,  merely  a small 
white  image  of  the  slit  in  the  window,  giving  thus  a proof, 


FIG.  126.— FORMATION  OF  COMPLEMENTARY  COLORS. 

See  page  331. 

in  addition  to  the  others  just  noticed,  that  all  the  colors 
together  make  white.  If  now  between  the  cylindrical  lens 
and  the  wall  a part  of  the  light  be  shut  off  by  means  of  a 
screen,  a colored  image  instantly  appears  upon  the  wall. 
If,  forshutting  off  this  part  of  the  light,  one  use,  cemented 
to  a plate  of  glass,  a prism  finer  than  a knife-blade,  and 
showing  therefore  no  sensible  dispersion  of  colors,  al- 
though its  power  of  refraction  remains,  it  will  divide  the 
rays  into  two  bands  which  will  form  two  images  on  the 
wall,  each  of  which  will  be  colored.  See  Fig.  125,  page 
330,  and  S — S in  Fig.  126. 


332 


PROPORTION  AND  HARMONY. 


In  such  cases  the  colors  depend  upon  where  the  rays 
are  divided.  Beginning  with  the  rays  that  produced  the 
red  end  of  the  spectrum  and  moving  the  dividing  prism 
gradually  toward  the  rays  that  produced  its  violet  end,  it 
is  found  that 

if  one  color  be  red  the  other  is  bluish-green  ; 

44  “ 44  44  orange  44  44  44  turquoise-blue  ; 

44  44  44  44  yellow  44  44  44  ultramarine-blue 

44  44  44  44  yellowish-green  44  44  44  violet  ; 

44  44  44  41  green  44  44  4 4 purple. 

These  then  are  the  two  colors  which  together  make  white, 
termed  for  this  reason  the  complementary  colors. 

They  are  not,  as  some  will  notice,  the  colors  which  in 
former  times  were  supposed  to  make  white.  Those  were 
derived  from  experiments  with  pigments  in  the  following 
way.  It  was  found  that  red,  yellow,  and  blue  paint  when 
mixed  together  made  white  or  rather  a whitish-gray.  It 
was  supposed  therefore  that  if  two  colors  were  to  be  used 
they  also,  in  order  to  represent  white,  should  be  com- 
pounded of  these  three  primitive  colors  as  they  were  called. 
Artists  therefore  took  as  their  complementary  colors 

red  and  green,  which  latter  they  had  found  could  be  formed  by  mixing  yellow  and  blue  ; 
yellow  and  purple,  44  44  44  44  44  44  44  44  44  44  blue  and  red  ; 

blue  and  orange,  44  44  44  44  44  44  44  44  44  44  red  and  yellow. 

The  German  physicist,  Helmholtz,  revealed  very  clearly 
the  erroneousness  of  this  supposition,  showing  that  the 
results  are  different  when  pigments  are  mixed  and  when 
the  colors  themselves  are  mixed.  It  was  noticed  that 
while  a combination  of  blue  and  yellow  pigments  makes 
green,  a blue  veil  spread  over  a yellow  ground,  and  seen 
from  a distance,  where  both  colors  blend,  makes  gray. 
So  vermilion  and  ultramarine  mixed  on  the  palette  pro- 
duce a reddish-brown,  but  vermilion  lines  on  a blue  ground 
seen  from  a distance  produce  purple.  Experiments  with 


THE  COMPLEMENTARY  COLORS. 


333 


pigments,  too,  showed  in  the  spectrum  of  Prussian  blue, 
a deficiency  of  light  at  the  red  end,  and  in  that  of  gamboge 
(yellow)  a like  deficiency  at  the  violet  end.  Both  spec- 
trums,  however,  did  contain  green.  So,  according  to  the 
principle  that  colors  transmit  or  reflect  rays  of  like  color 
with  themselves  (see  page  314),  the  result  of  mixing  the 
two  was  to  obtain  green,  a result  which  had  to  do  with  the 
particular  ingredients  and  colors  of  these  particular  pig- 
ments, but  not  with  colors  in  the  abstract.  It  did  not 
warrant  a general  rule  to  the  effect  that  blue  and  yellow 
make  green.  Similar  tests  with  other  pigments  have 
revealed  that  nothing  can  be  known  certainly  of  the 
colors  produced  by  mixing  them  until  a mixture  has 
actually  been  made.  On  the  contrary,  if  colors  be  mixed 
as  is  done  when  by  their  effects  on  the  eye  two  are  made 
to  seem  like  one,  either  because  a fabric  of  one  color  is 
placed  over  another  of  a different  color,  or  because  lines 
of  one  color  are  painted  over  another  color,  or  because  the 
colors  of  two  spectrums  are  made  to  intersect,  or  because 
two  colors  are  made  to  revolve  in  the  color  top, — in  all 
these  cases  the  result  has  been  found  to  be  determined  by 
a fixed  law.  In  accordance  with  this  law,  the  colors 
making  white  have  been  found  to  be  not  those  formerly 
supposed  to  be  complementary,  but  the  others  that  have 
just  been  mentioned. 

Von  Bezold’s  “Theory  of  Color”  contains  the  chart 
in  Fig.  127,  page  334.  In  this  chart  the  colors  are  so  ar- 
ranged that  those  complementing  each  other  are  always 
at  two  ends  of  a diameter  drawn  exactly  through  the 
circle’s  centre.  It  is  one  of  many  charts  of  the  kind  ; but 
is  much  more  simple  in  construction  than  are  most  of 
them  and,  therefore,  is  much  more  easy  to  understand 
and  apply. 


334 


PROPORTION  AND  HARMONY. 


Let  us  consider  some  facts  which  this  chart  illustrates. 
It  shows  us  that  of  two  complementary  colors,  one — say  yel- 
low— is  usually  brighter  than  the  other — say  ultramarine. 
As  intimated  on  page  31 1,  all  the  colors  can  become  darker 
or  lighter  without  changing  their  hue  ; but  it  is  suggested 
by  this  chart  that  if  a color  becomes  darker,  its  com- 


60 


FIG.  127.— VON  BEZOLD’S  COLOR-CHART. 

See  pages  333-336,  390-393,  398,  403,  44. 


plementary,  in  order  that  the  two  together  may  still  con- 
tinue to  make  white,  must  become  correspondingly  lighter. 
This  suggestion  is  confirmed  by  an  experiment  with  a 
color  top  ; two  equal  parts  of  the  disk  of  this,  which,  when 
they  revolve  together,  form  white  or  gray,  continue  to  do 
the  same  if  we  put  a piece  of  black  over  part  of  the  red 
and  also  a piece  of  white  of  equal  size  with  the  black  over 


GREEN  COLOR. 


335 


part  of  the  green.  Accordingly  if  when  using  pigments 
black  be  mixed  with  one  complementary  color,  the  balance 
between  the  two  can  be  preserved  by  mixing  white  with 
the  other.  It  needs  to  be  borne  in  mind,  too,  that  white 
and  black  pigments  used  by  themselves  have  effects 
analogous  to  those  of  color,  the  white  being  necessarily 
many  degrees  darker  than  white  light,  and  the  black  many 
degrees  lighter  than  absolute  darkness. 

Another  fact  that  needs  to  be  noticed  is  that,  inasmuch 
as  every  shade  and  tint  of  every  color,  and  not  only  so, 
but  every  mixture  of  the  shades  and  tints  of  different 
colors,  has  its  own  peculiar  complementary  shade  or  tint 
or  mixture,  the  possible  number  of  complementary  pairs 
of  color-effects  is  practically  infinite.  But  it  must  not  be 
supposed  that,  because  complementary,  all  of  these  pairs 
are  agreeable  or  beautiful.  An  ugly  mixed  color  may 
have  an  ugly  mixed  complementary.  The  two  together 
may  fulfil  certain  laws  of  harmony,  as  may,  so  far  as  con- 
cerns effects  of  pitch,  the  notes  of  a cymbal  and  a kettle- 
drum. But  neither  the  colors  in  the  one  case,  nor  the 
sounds  in  the  other,  fulfil  all  the  laws  of  harmony.  Each 
of  the  factors  constituting  each  pair  is  inharmoniously 
mixed.  Two  color-effects  used  together,  therefore,  even 
when  complementary,  are  not  necessarily  beautiful,  except 
when  they  are  pure,  or  are  the  tints  or  shades  of  pure 
colors;  that  is,  of  pure  hues  mixed  with  only  pure  bright- 
ness or  pure  darkness. 

The  chart  reveals,  too,  that  between  violet,  purple,  and 
red  there  are  differences  in  degree  by  no  means  matched 
by  the  differences  between  their  complementaries,  yellow- 
ish-green and  bluish-green.  This  fact  makes  the  difficulty 
of  using  green  with  its  proper  contrasts  very  great ; and 
this  difficulty  becomes  still  greater  in  view  of  the  position 


336 


PROPORTION  AND  HARMONY. 


of  green  on  the  dividing  line  between  the  warm  and  cold 
colors,  concerning  the  entirely  different  uses  of  which  in 
sunshine  and  shadow  mention  was  made  on  page  320.  We 
see  one  reason,  therefore,  why  a decisive  test  of  a good 
landscape  painter  is  the  way  in  which  he  manages  his 
greens,  as  well  too,  perhaps,  as  why  decorators  in  all  times 
have  made  but  a limited  use  of  them. 


CHAPTER  XX. 


PHYSICAL  AND  PHYSIOLOGICAL  CORRESPONDENCES 
BETWEEN  HARMONY  IN  MUSIC  AND  PAINTING. 

Study  of  Color-Effects  in  the  Eye  itself — Not  as  far  Advanced  as  the  Study 
of  Sound-Effects  in  the  Ear  ; Facts  Known  with  Reference  to  the 
Effects  of  Amplitude  and  Rate  of  Sound-Waves — Of  their  Form — 
Compound  Waves — Determining  Quality — Partial  Tones — Their  In- 
fluence upon  Harmony,  Simultaneous  and  Successive- — Correlation  of 
Rhythm  and  Harmony  ; the  Latter’s  Physiological  Effect — Foster’s 
Explanation — Correspondences  between  Vibratory  Effects  in  the  Ear 
and  in  the  Eye — Differences  between  them — Inferences  from  the 
Minuteness  of  Color-Waves — -Two  Main  Questions  Involved  in  the 
Discussion  of  Color-Harmony. 

XPERIMENTS  made  with  color  as  it  appears  in  the 
external  world  have  naturally  been  supplemented, 
as  knowledge  has  progressed,  by  endeavors  to  ascertain 
the  influence  exerted  upon  it  in  the  eye  itself;  and  before 
we  can  go  on  intelligently  to  develop  the  relations  to  color- 
harmony  of  the  facts  brought  out  in  the  preceding  chapter, 
we  must  consider  this  latter  subject.  As  was  said  on 
page  307,  too,  what  has  been  learned  concerning  it  has  of 
late  years  almost  revolutionized  the  practical  methods  of 
painting,  the  aim  of  the  modern,  as  distinguished  from 
the  older  artist,  being  to  use  pigments  with  reference  to 
the  way  in  which  they  shall  mix,  as  is  said,  in  the  act  of 
perception  in  the  eye.  No  further  proof  is  needed  to 
show  the  practical  bearing  upon  art  of  conceptions  that 
may  be  held  with  reference  to  the  subject  that  is  to  be 
discussed  in  the  present  chapter. 


338 


PROPORTION  AND  HARMONY. 


It  is  well  to  notice,  also,  that  the  study  of  color  has  not 
yet  advanced  as  far  as  that  of  sound.  The  main  reason 
for  this,  perhaps,  is  the  fact  that  it  is  more  easy  to  come 
to  conclusions  concerning  vibrations,  say,  of  32  per  second , 
which  are  in  the  region  of  those  considered  necessary  to 
the  least  multiplied  force  causing  a musical  tone,  than 
concerning  the  458,000,000,000,000 per  second , which  are  in 
the  region  of  those  considered  necessary  to  the  least  mul- 
tiplied force  causing  a hue.  The  same  reason,  too,  makes 
it  natural  and  sensible  for  us  here,  while  studying  the  ef- 
fects of  color,  to  take  suggestions  from  the  course  generally 
pursued  by  others  when  tracing  out  analogous  facts  with 
reference  to  sounds.  As  we  turn  to  do  this,  it  will  be 
noticed  that,  in  the  case  of  sounds  as  well  as  of  colors,  the 
earliest  experiments  were  confined  to  conditions  supposed 
to  be  manifested  in  the  external  world.  It  was  through 
comparing  the  sounds  of  cords  of  different  lengths  that 
the  Pythagorean  system,  based  upon  ratios  determining 
the  relations  between  harmonic  tones,  was  first  developed. 
Only  of  late  years  has  it  been  conceived  that  there  is  a 
physiological  principle  deeper  than  that  of  these  ratios, 
of  which  they  are  a result,  not  a cause.  Exactly  what 
this  principle  is,  has  not  yet  been  indisputably  determined. 
But  three  facts  with  reference  to  the  subject  are  gen- 
erally acknowledged  (see  Chapter  XIV.  of  “ Rhythm 
and  Harmony  in  Poetry  and  Music  ”) : First,  that  degrees 
of  loudness  are  determined  by  the  relative  amplitude  of 
vibrations.  A string  of  a certain  texture  and  length  will 
produce  a loud  sound  in  the  degree  in  which  it  is  struck 
violently,  and,  therefore,  caused  to  cover  a greater  space 
with  its  vibrations.  The  second  fact  is,  that  degrees  of 
pitch  are  determined  by  the  relative  time  of  vibrations. 
A string  shortened  in  length,  and  therefore  vibrating  more 


HARMONY  IN  MUSIC. 


339 


rapidly,  will  produce  a higher  tone.  It  was  from  this  fact 
that,  by  very  simple  experiments,  the  law  was  discovered 
that  harmonic  tones  are  related  to  one  another  accord- 
ing to  certain  definite  ratios. 

After  physicists  had  proved  that  degrees  of  loudness 
in  sound  are  determined  by  the  amplitude  of  vibrations, 
and  degrees  of  pitch  by  the  time  of  vibrations,  they  felt 
that  nothing  was  left  to  determine  the  quality  of  sounds 
except  the  forms  of  vibrations.  It  was  easy,  too,  for 
them  to  imagine  that  these  should  differ  in  form.  For 
instance,  when  a bow  is  drawn  across  the  strings  of  a 
violin,  it  may  fall  upon  them,  giving  them  an  up-and- 
down  motion  ; it  may  move  over  them,  giving  them  a 
motion  from  side  to  side  ; it  may  turn  them,  giving  them 
a twisting  motion  ; it  may  bound  over  them,  giving  them 
a jarring  motion;  or  it  may  do  all  these  together;  be- 
sides which,  wherever  it  touches  the  strings  it  may  check 
the  movements  caused  by  vibrations  of  their  entire  length, 
and  cause  smaller  waves  between  the  points  where  they 
are  played  upon  by  the  bow  and  where  they  are  attached 
to  the  violin.  According  to  a similar  mode  of  reasoning, 
it  was  natural  to  suppose  that  the  waves  of  sound  pro- 
duced by  a wind  instrument,  a trumpet,  or  a human 
throat,  for  instance,  deviated  as  they  are  from  a straight 
course  by  a number  of  curves  and  angles,  must  necessarily 
be  more  or  less  compound  as  they  emerge  from  the  instru- 
ments; and,  being  so,  must  differ  in  form  for  different 
kinds  of  instruments.  Considerations  of  this  sort  caused 
investigations  to  be  made  into  the  forms  of  vibrations ; 
and  by  means  of  very  ingenious  expedients, — by  magni- 
fying, for  example,  the  vibrations  of  a cord  or  pipe,  and 
making  them  visible,  through  using  an  intense  ray  of 
light  to  throw  an  image  of  them  upon  a canvas  in  a 


340 


PROPORTION  AND  HARMONY. 


darkened  room, — the  forms  assumed  by  the  vibrations 
caused  by  many  of  the  ordinary  musical  instruments  have 
been  accurately  ascertained.  These  forms  have  been 
resolved,  according  to  well-known  mathematical  princi- 
ples, into  their  constituent  elements.  For  instance,  if 
the  form  of  vibration  be  as  in  the  first  of  these  examples, 
it  may  be  resolved  into  the  forms  that  are  in  the  second. 


In  short,  investigations  of  this  character  have  shown 
that  musical  sounds  may  result,  and  usually  do  result,  not 
from  simple  but  from  compound  forms  of  vibrations; 
that  is  to  say,  in  connection  with  the  main  waves  there 
are  other  waves.  All  of  these  are  not  invariably  present, 
but  when  present  they  are  related  to  the  main  wave — i.  e., 
in  tones  that  make  music  as  distinguished  from  noise — 
as  2:  1,3:  1,4:  1,  5 ; 1,6:  1,7:  1,8:  1,9:  1,  and  even  in 
some  cases  as  10:  1.  In  other  words,  these  smaller  ac- 
companying waves  vibrate  two,  three,  and  four  times, 
and  so  on  up  to  ten  times,  while  the  main  wave  is  vibrat- 
ing once.  But  this  is  not  all.  The  sounds  of  these  com- 
pound vibrations  have  been  analyzed.  By  means  of 
instruments  like  Helmholtz’s  resonators,  which  are  small 
brass  boxes  or  globes  each  made  of  such  a size  as  to 
respond  sympathetically  to  a certain  pitch,  it  has  been 
found  that  each  form  of  vibration  represented  in  a note 
produces  a separate  pitch  of  its  own.  When,  therefore, 


34i 


HARMONY  IN  MUSIC. 

a tone  is  sounded  on  a violin,  we  hear  in  it  not  only  the 
pitch  caused  by  the  vibrations  of  the  whole  length  of  the 
string,  but  also  in  connection  with  it  a number  of  other 
partial  tones,  as  all  the  constituents  of  any  one  note  are 
called,  each  of  which  has  its  own  pitch,  produced  by 
vibrations  of  one  half,  one  third,  one  fourth,  etc.,  of  the 
length  of  the  string. 

The  difference  in  the  number,  the  combination,  and 
the  relative  loudness  of  these  partial  tones  in  a musical 
sound  is  what  determines  its  quality  or  timbre.  In  instru- 
ments like  kettle-drums,  cymbals,  or  bells,  one  side  is 
almost  invariably  thicker  than  the  other.  For  this  reason, 
the  main  vibrations  are  not  uniform,  and,  of  course,  the 
partial  tones  cannot  be  so.  Such  instruments,  accord- 
ingly, are  less  musical  than  noisy,  and  are  used  on  only 
exceptional  occasions.  But  in  ordinary  musical  sounds 
the  partial  tones,  if  present  at  all, — they  differ  as  produced 
by  different  instruments, — are  indicated  in  the  notation 
below.  Notice  that  the  prime  tone  is  counted  as  the  first 
partial  tone ; also  that  the  second,  fourth,  and  eighth 
partials  are  the  same  as  the  prime  tone  with  exception  of 
being  in  higher  octaves. 

Partial  tones  Of  F,  of  which  C is  Of  G,  which  itself  is 

of  the  pitch  the  third  and  near-  the  third  and  nearest 

of  C est  partial  partial  of  C 


The  notes  that  are  used  ( ^ T f £ C ),  in  the  degree  in 


342 


PROPORTION  AND  HARMONY. 


which  they  are  long,  indicate  tones  which  the  reader  needs 
most  to  notice;  and  the  marks  after  the  letters  indicate 
the  relative  distance  of  a tone  from  the  octave  of  the 
tone  which  is  the  standard  of  pitch.  C',  F',  or  G',  for 
instance,  are  one  octave  below  C,  F,  or  G,  and  these  are 
one  octave  below  c,  f,  or  g,  and  two  octaves  below  c', 
{',  or  g'. 

In  “Rhythm  and  Harmony  in  Poetry  and  Music”  it 
was  shown  that  tones — though  they  may  be  in  different 
octaves — which  are  related  to  one  another  in  pitch  as 
are  the  partial  tones  nearest  the  fundamental  bass,  form  the 
musical  chords — as  do,  in  the  first  measure  on  page  341, 
C,g,  and  e,  with  the  addition  also,  if  we  include  the  chord 
of  the  seventh,  of  b flat.  But  because  b flat  is  distant 
from  the  fundamental  bass,  the  chord  containing  it  is 
sometimes  wrongly  called  a discord.  It  was  shown,  too, 
that  these  same  partial  tones  in  connection  with  the 
partial  tones  of  G and  F which  are  nearly  related  to  C, 
form  the  notes  of  the  musical  scale.  See  the  music  on 
page  343.  When  we  speak  of  musical  harmony,  we  some- 
times refer  to  the  effect  of  a single  chord  whose  notes  are 
sounded  simultaneously.  But  we  also  refer  to  the  effects 
of  many  different  chords  when  they  are  sounded  succes- 
sively. In  other  words,  harmony  in  music  consists  not 
only  in  using  harmonic  chords,  but  in  passing  from  one 
chord  to  another ; and  the  principles  of  harmony,  as 
determined  by  this  latter  requirement,  necessitate  using 
chords  in  succession  that  contain  (as  they  almost  in- 
variably do)  some  prime  tone,  or  else  some  partial  tone, 
that  is  the  same.  See  pages  2 13-2 17  of  “Rhythm  and 
Harmony  in  Poetry  and  Music.”  Therefore,  whether  ap- 
plied to  simultaneous  or  to  successive  chords,  the  system 
of  musical  harmony,  as  it  has  developed,  is  merely  a pro- 


CAUSES  OF  MUSICAL  HARMONY. 


343 


cess  of  putting  together,  according  to  the  methods  in 
the  chart  on  page  3,  vibrations  that  are  alike  or  are 
related,  in  that  they  are  multiples  or  subdivisions  of  some 
single  standard  of  measurement.  The  following,  for 
instance,  represents  the  usual  method  of  harmonizing 
the  notes  of  the  musical  scale.  In  every  chord  it  will 


1 „ 

\=rZb 

re 

nn  1 fa 

— — 
sol 

la  si 

3= 

do 



, 

i — 

i =) 

& e 

c 

G 

C F 

c 

F G 

c 

be  noticed  that  at  least  one  prime  tone  is  repeated  from 
the  chord  preceding  it.  The  fact  that  the  same  method 
is  really  fulfilled  even  when  it  is  only  a partial  tone  that 
is  repeated,  is  that  which  justifies  the  occasional  abrupt 
transitions  with  which  we  are  all  familiar.  Of  course,  the 
partial  tone  used  in  such  cases  must  be  very  near  the 
fundamental  bass — i.  e.,  between  the  first  and  the  fifth — - 
or  the  ear  will  not  detect  between  the  successive  chords 
any  harmonic  relationship  whatever. 

The  reader  will  not  fail  to  notice  that  the  effects  of 
harmony  as  thus  described  are,  in  important  regards, 
analogous  to  those  of  rhythm,  and  yet  of  a rhythm  so 
finely  grained  that  it  is  impossible  that  the  mind  should  be 
conscious  of  its  constituent  elements.  In  rhythm  the 
beats  determining  the  measures  necessitate  the  use  of  fac- 
tors— i.  e.,  notes — that  go  into  one  another  or  into  some 
third  factor  a certain  equal  number  of  times  : in  harmony 
the  vibrations  determining  the  different  degrees  of  pitch 
do  the  same.  It  is  sometimes  said  that,  as  the  mind  con- 
sciously counts  the  beats  in  determining  rhythm,  so,  in 
some  subtle  way,  it  unconsciously  counts  the  vibrations 


344 


PROPORTION  AND  HARMONY. 


in  determining  harmony.  But  is  it  necessary  to  suppose 
this?  When  influenced  by  tones  that  seem  consonant  we 
are  certainly  not  conscious  of  counting.  Are  we  con- 
scious of  doing  it  even  when  influenced  by  the  effects  of 
rhythm  ? Are  we  conscious  of  anything  except  of  cer- 
tain accentuations  of  tone  that  are  equally  subdivided 
into  other  accentuations — all  of  which,  in  some  way,  are 
so  related  that  they  exactly  fit,  the  smaller  into  the  larger 
and  all  into  the  largest  ? And  if  we  need  not  count  the 
accents  in  rhythm,  why  should  we  do  it  in  harmony? 
Why  need  we  do  more  than  experience  certain  throbs 
or  thrills  of  sound  equally  subdivided  into  other  thrills, 
all  of  which  are  so  related  that  they  exactly  fit,  the  smaller 
into  the  larger  and  all  into  the  largest  ? As  a result  of  ex- 
periencing these,  every  part  of  the  auditory  organism,  under 
any  influence  of  sound,  is  under  the  same  influence, — as 
much  so  as  is  every  part  of  a still  pool  when  we  have  thrown 
a single  stone  into  it,  infinitely  varied  as  may  be  the  sizes 
of  different  waves  that  in  remote  places  circle  into  ripples. 
The  result,  inasmuch  as  all  the  sound-waves  represent  a 
single  impulse,  is  an  unimpeded,  free,  regularly  recurrent 
vibratory  glow  of  the  whole  auditory  apparatus.  But  if, 
on  the  contrary,  the  effect  resemble  that  upon  the  waters 
of  a pool  when  more  than  one  stone  is  thrown  into  it,  i.  e., 
if  the  sound-waves  do  not  coalesce,  if  the  smaller  do  not 
fit  into  the  larger,  and  all  together  into  the  largest,  then 
nothing  ensues  but  a broken,  impeded,  constrained,  irregu- 
lar series  of  jolts  or  jars.  The  difference  in  the  ear 
between  the  sensation  of  harmony  and  of  a lack  of  it,  is  the 
physical  difference  between  thrilling  or  glowing  and  jolt- 
ing or  jarring.  Notice,  too,  that  this  illustration  applies  to 
notes  when  sounding  not  only,  as  in  one  chord,  simulta- 
neously, but,  as  in  different  chords,  successively.  Two 


CAUSES  OF  MUSICAL  HARMONY. 


345 


things  related  to  the  same  thing  cannot  fail,  in  some  way, 
to  be  related  to  each  other  ; and  two  chords,  each  contain- 
ing sets  of  vibrations  for  which  there  is  a common  multi- 
ple, and  both  containing  one  set  of  vibrations  ( i . e.,  one 
tone)  which  is  the  same,  must  both  be  entirely  composed 
of  vibrations  for  which  there  is  some  common  multiple. 
This  common  multiple,  moreover,  for  the  vibrations  of  a 
first  and  second  chord  may  be  different  from  that  of  the 
vibrations  of  the  second  and  third  chord.  It  is  possible, 
therefore,  for  a series  of  chords,  each  in  part  repeating 
the  same  tones  as  the  last  sounded,  and  in  part  introdu- 
cing new  tones,  to  change,  very  soon,  the  whole  character 
of  the  general  vibratory  effect  ; and  yet  if  this  be  done 
with  sufficient  gradualness,  the  auditory  apparatus  will 
experience  no  jolt  or  jar,  while,  at  the  same  time,  it  will 
be  conscious  of  constant  progress  and  so  of  relief  from 
anything  resembling  monotony. 

That  the  illustrations  just  used  to  represent  the  effects 
experienced  in  the  ear  have  a scientific  justification  may  be 
shown  by  a quotation  from  Foster’s  “ Text-Book  of  Physi- 
ology,”  § 850.  “ A complex  sound,”  he  says,  “ consisting 

of  vibrations  of  more  than  one  period,  travels,  as  we  have 
said,  not  as  a group  of  discrete  waves,  each  corresponding 
to  a vibration  of  a particular  period,  but  as  a complex 
wave  in  which  the  simple  waves  are  compounded  into  one  ; 
and  the  vibrations  of  the  tympanic  membrane  (i.  e.,  the 
external  ear-drum),  followed  by  the  vibrations  of  the 
perilymph  (i.  e.,  the  fluid  behind  the  drum  through  which 
the  vibrations  pass),  have  the  same  composite  character. 
When,  for  instance,  a note  is  sung,  or  sounded  on  a musi- 
cal instrument,  the  air  in  the  external  auditory  passage  is 
not  the  subject  of  one  set  of  waves  corresponding  to  the 
fundamental  tone,  and  of  other  sets  corresponding  to  the 


346 


PROPORTION  AND  HARMONY. 


several  partial  tones,  but  vibrates  in  the  pattern  of  one 
composite  wave.  The  tympanic  membrane  executes  one 
complex  vibration,  and  a corresponding  vibration  excites 
the  auditory  epithelium  (i.  e.,  the  nerve-cells).  And  this 
holds  good  not  for  a single  sound  only,  but  for  a mixture 
of  sounds.  We  can,  in  a clumsy  way,  take  a graphic 
record  of  the  vibrations  of  a dead  tympanic  membrane  by 
attaching  a marker  to  the  stapes  ; could  we  take  an  ade- 
quate record  of  the  movements  of  the  living  tympanum 
of  one  of  the  audience  at  a concert,  we  should  obtain  a 
curve,  a phonogram,  which,  though  a single  curve  only, 
would  be,  on  the  one  hand,  a record  of  the  multitudinous 
vibrations  of  the  concert,  and,  on  the  other  hand,  a pic- 
ture of  the  actual  blows  with  which  the  perilymph  {i.  e.,  the 
fluid  behind  the  ear-drum)  had  struck  the  auditory  epi- 
thelium.” Foster  then  goes  on  to  say,  as  indicated  by 
the  fact  that  we  can  often  detect  the  different  instru- 
ments at  play  in  an  orchestra,  by  the  minute  organs  at 
the  ends  of  the  auditory  nerve,  that  it  is  probable  that, 
after  reaching  these,  “ the  complex  vibration  is  analyzed 
again  into  its  constituent  simple  yibrations,  that  the  vibra- 
tions start  afresh,  so  to  speak,  in  the  auditory  epithelium, 
marshalled  in  the  same  array  as  that  in  which  they  started 
from  the  sounding  instruments,  as  if  the  auditory  epi- 
thelium itself  constituted  the  band  playing  the  music.” 
It  is  interesting,  too,  to  recall,  in  this  connection,  that  in- 
vestigations made  with  the  microscope  upon  the  nerve- 
fibres  and  cells  of  living  beings,  in  the  lower  orders  of  life, 
have  proved  that  the  sensations  of  touch,  at  least,  when 
communicated  through  the  nerves,  pass  through  them  in 
the  forms  of  waves.  As  the  auditory,  like  the  optic,  nerve 
is  merely  a bundle  of  nerve-fibres,  each  of  which,  appar- 
ently, is  connected  with  a separate  termination,  we  can 


COLOR-HARMONY  AS  RELATED  TO  MUSLCAL.  347 


apprehend  the  reasonableness  of  Foster’s  conclusion. 
Exactly  what  is  each  particular  function  of  each  of  these 
minute  terminating  fibres,  however,  has  not  yet  been  defi- 
nitely determined  ; the  formerly  accepted  theory  that  each 
of  Corti’s  rods,  of  which  there  are  several  thousand  in  the 
ear,  is  fitted  to  respond  sympathetically  to  a particular 
pitch  having  been  abandoned,  largely  because  such  rods 
are  not  discoverable  in  the  ears  of  birds. 

With  reference  to  color,  certain  deductions,  in  all  regards 
analogous  to  those  made  with  reference  to  sounds,  are 
now  acknowledged  to  be  justified.  It  is  acknowledged 
that  intensity  of  vibrations  must  determine  the  degrees 
of  the  brightness  of  the  color,  that  rate  or  time  of  vibra- 
tions must  determine  its  hue,  and  that  form  or  shape  of 
vibrations  must  determine  its  composition  or  mixture. 
From  those  deductions  it  would  seem  to  follow — though 
it  cannot  be  said  to  be  generally  acknowledged — that  only 
such  forms  of  vibrations  can  harmonize  as  can  coalesce 
in  the  retina.  In  Chapter  XIX.  we  found  that  all  colors 
result  from  subdivisions  of  a ray  of  white  light,  also  that 
white  light  can  always  be  exactly  subdivided  into  any  two 
of  the  colors  called  complementary.  From  this  the  con- 
clusion seems  to  be  warranted,  that  both  for  the  vibrations 
causing  white  light  and  also  for  those  causing  each  of  any 
two  complementary  colors  so  far  as  they  are  thus  pro- 
duced, there  must  be  some  common  multiple.  There- 
fore, when  the  three  are  put  together,  all  their  different 
vibrations,  like  all  the  notes  of  a measure  in  rhythm,  can  go 
some  exact  number  of  times  into  this  common  multiple. 
In  other  words,  harmony  would  result,  as  in  the  case  of 
music,  from  putting  together  vibrations  that  are  alike,  or 
are  related,  in  that  they  are  multiples  or  subdivisions  of 
some  single  standard  of  measurement,  or,  as  expressed  in 


348 


PROPORTION  AND  HARMONY. 


“ The  Genesis  of  Art-Form,”  by  putting  together  complex 
wholes  that  have  like  partial  effects.  Once  more  the 
hypothesis  seems  to  be  warranted  that,  just  as  in  the  ear, 
when  different  sounds,  as  the  scraping  of  the  bow,  the 
twanging  of  the  string,  and  the  resonance  of  the  body  of 
a violin,  are  blended  into  a single  mixed  effect,  it  is  im- 
possible to  analzye  and  separate  the  different  elements,  so 
there  are  certain  blendings  of  colors  that  the  eye  cannot 
analyze.  The  mixed  effects  appeal  to  the  senses  as  a 
simple,  single  effect.  When,  however,  the  differences 
between  the  constituent  elements  become  slightly  greater, 
as  in  the  case  of  chords,  especially  as  produced  upon  differ- 
ent instruments,  or  as  in  the  case  of  a general  impression 
of  one  color  produced  by  a checkered  or  a plaided  texture, 
the  result  is,  at  once,  recognized  to  be  complex,  and  the 
factors  of  its  composition  can  be  more  easily  determined. 

Notice,  however,  that  there  are  certain  differences  be- 
tween distinguishing  the  elements  in  sounds  and  insights. 
When  separating  the  notes  even  of  a single  chord,  we  do 
this  mainly  in  the  order  of  time,  i.e.,  by  successively  direct- 
ing attention  first  to  the  one  note  and  then — of  course  by  a 
very  rapid  change — to  the  other.  We  recognize  first  that 
this  is  C,  and  then  that  that  is  G,  and  so  on.  On  the  con- 
trary, we  distinguish  colors  mainly  in  the  order  of  space, 
by  perceiving  and  examining  them  as  we  compare  one 
with  another  that  adjoins  it.  This  distinction  between 
the  actions  of  the  ear  and  of  the  eye  becomes  still  more 
marked  when  we  consider  the  phase  of  harmony  in  color 
which  is  analogous  to  that  produced  in  music  not  by  simul- 
taneous but  by  successive  tones.  That  which  in  sight  is 
analogous  to  this  latter  is  the  movement  which  the  eye 
itself  makes  in  examining  first  one  part  of  a scene  and 
then  a different  part  of  it. 


PHYSIOLOGICAL  CAUSE  OF  COLOR-HARMONY.  349 


Sound-waves  are  comparatively  large.  The  quotation 
from  Foster  on  page  345,  suggests  that  we  can  conceive  of 
each  successive  set  of  complex  waves  as  agitating  every 
part  of  the  ear-drum.  When  the  sound  represented  by 
this  complex  wave  is  succeeded  by  a different  sound 
represented  by  a different  complex  wave,  the  first,  ac- 
cording to  the  laws  of  music,  is  made  harmonious  to  the 
second  by  having  both  contain  a number  of  like  kinds  of 
vibrations,  producing  a like  partial  tone.  As  this  fact  was 
expressed  in  “ Rhythm  and  Harmony  in  Poetry  and 
Music,”  the  complex  wholes,  i.  e.,  in  this  case  the  chords 
which  are  put  together,  have  “ like  partial  effects.”  Color- 
waves  are  exceedingly  small.  This  we  might  infer,  if 
from  nothing  else,  from  the  fact  that  it  is  necessary  to 
have,  at  every  minutest  point  on  the  retina  upon  which 
the  external  scene  is  impressed,  an  exact  representation 
of  some  part  of  the  scene,  and  that  the  color  of  this 
part  may  differ  greatly  from  that  of  the  part  beside 
it.  These  color-waves,  indeed,  are  so  small  that,  notwith- 
standing an  existing  theory  to  the  contrary,  it  must  seem  to 
many  impossible  to  conceive  that  any  one  set  of  them  (i.  c., 
any  one  color),  however  complex  in  form,  can  influence 
more  than  a very  minute  part  of  the  retina,  unless,  of 
course,  accompanied  by  many  other  sets  exactly  like  them- 
selves. What  is  meant  by  suggesting  that  these  waves 
may  influence  a minute  part  of  the  retina,  will  be  under- 
stood when  it  is  added  that,  according  to  Le  Conte  in  his 
“ Sight,”  there  are  in  the  centre  of  the  retina,  in  a space 
not  larger  than  one  tenth  of  an  inch  square,  no  less  than  a 
million  cones.  (Compare  Fig.  128,  page  350,  with  Figs. 
130,  page  380,  and  131,  page  381.)  As  is  known,  too,  all 
these  are  so  connected  with  their  surroundings,  as  Foster 
says,  by  a “ basket-work  ” or  “ sponge-work,”  that  they  are 


350 


PROPORTION  AND  HARMONY. 


apparently  capable  of  vibratory  motion.  If  their  minute 
vibrations  as  affected  by  movements  in  the  ether,  may  be 
supposed  to  influence  the  whole  retina  in  any  degree,  how 
can  they  do  so  except  as  one  set  of  waves  may  be  sup- 
posed to  influence  the  whole  surface  of  a sea?  On  the 
same  sea  there  may  be  breezes  causing  waves  differing, 
as  these  vibrations  do,  in  intensity,  in  rate,  and  in  shape. 

But,  in  case  these  differ- 
ences were  far  apart,  and 
produced  by  very  gradual 
changes  from  one  form  to 
another,  there  might  be, 
to  an  eye  capable  of  per- 
ceiving the  whole  surface 
at  once,  no  appearance 
whatever  of  inharmonious 
action.  It  needs  to  be 
added,  however,  that,  within  the  narrow  limits  of  a picture, 
it  is  impossible  for  any  colors  to  be  very  widely  separated, 
and,  not  only  so,  but  that,  even  if  they  could  be,  the  eye, 
in  shifting  attention  from  one  point  to  another  while  ex- 
amining them,  would  constantly  be  bringing  them  into  still 
closer  proximity,  in  fact  necessitating  often  the  perception 
of  all  the  colors  on  the  canvas  by  exactly  the  same  part 
of  the  retina. 

These  latter  conditions,  taken  in  connection  with  those 
mentioned  on  page  349,  will  show  us  that,  in  considering 
the  harmony  of  color,  there  are  two  main  questions  to  be 
discussed  : first,  the  selection  and  arrangement  of  colors 
with  reference  to  their  general  effects  in  a painting  con- 
sidered as  a whole,  corresponding  to  the  selection  in  music 
of  a key-note,  involving  that  of  the  particular  scale  and 
chords  that  go  with  it  ; and,  second,  the  selection  and 


A C 


FIQ.  128.— CONES  AND  RODS  IN  DIFFER- 
ENT PARTS  OF  THE  RETINA. 

A , usual  surface  ; B , raised  margin  of  central 
yellow  spot  ; C,  surface  of  central  spot. 

See  pages  349,  350,  381. 


COLOR  LI A R MON  Y. 


351 


arrangement  of  colors  with  reference  to  their  special 
effects  when  placed  side  by  side,  together  with  the  ways  of 
sufficiently  separating  and  yet  connecting  them  in  cases  in 
which  placing  them  side  by  side  would  produce  discord. 
This  phase  of  harmony  corresponds  to  what  in  music  is 
termed  modulation  or  transition  from  one  key  to  another. 
The  first  of  these  questions  will  naturally  be  discussed 
while  considering  the  methods  in  the  chart  on  page  3 pre- 
ceding consonance,  and  the  second  while  considering  con- 
sonance and  the  methods  following  it. 


CHAPTER  XXI. 


GENERAL  EFFECTS  OF  COLOR  IN  PAINTINGS  CONSID- 
ERED AS  WHOLES. 

Artistic  Harmony  not  Imitated  from  Nature — Field-Theory  with  Reference 
to  the  Method  of  Securing  it — Physiological  Objection  to  it — Psycho- 
logical— Principality,  Subordination  : Tone — Harmony,  whether  Due  to 
Similarity,  as  in  Tone,  or  to  Variety,  an  Exemplification  of  Similar 
Physiological  Requirements — Analogy  from  Music  and  the  Key-Note — 
Balance  and  Organic  Form — Their  Effects  both  Psychical  and  Physio- 
logical— Congruity  as  Representing  Conceptions  and  Conditions — In- 
congruity, Comprehensiveness,  Central-Point,  Setting,  and  Parallelism 
— Symmetry — Repetition — Alteration,  Alternation — Massing,  Breadth, 
or  Chiaroscuro — Its  Relation  to  Principality  and  Balance — And  Other 
Methods — Interspersion,  Complication,  and  Continuity. 


S suggested  on  page  297,  it  must  always  be  borne  in 


mind  that  harmony  in  art  is  not  necessarily  pro- 
duced by  copying  nature.  In  this,  all  possible  colors  are 
found  side  by  side  ; and  many  of  their  combinations  are 
not  beautiful.  Of  course  in  the  narrower  compass  of  a 
painting,  where  all  may  be  seen  in  a single  act  of  vision, 
they  may  appear  still  less  so.  The  colors  in  paintings  are 
selected  colors.  The  question  before  us  is,  How  shall  they 
be  selected  in  order  to  secure  harmonious  effects? 

The  facts  discovered  with  reference  to  the  complement- 
ary colors,  as  described  in  Chapter  XIX.,  have  led  to  the 
natural  supposition  that  the  eye  takes  pleasure  in  seeing 
these  two  together  ; and  as,  in  all  cases,  the  two  have 
been  discovered  to  make  white,  it  has  been  supposed  that 
a theory  of  color-harmony  could  be  based  on  this  fact. 


352 


COL  OR-HARMON  V IN  PA  IN  TINGS  A S WHOLES.  353 

Any  two  colors  and,  therefore,  any  three  or  more  colors 
making  white  have  been  supposed  to  be  sufficient  to 
cause  harmony.  Moreover,  in  order  to  cause  this,  it  has 
even  been  supposed  by  some  that  it  is  necessary  to  have 
them  introduced  into  a painting  in  just  such  proportions 
as  to  make  white.  This  was  the  conclusion  reached  by 
the  English  physicist  Field,  in  what  is  termed  the  Field- 
theory.  For  instance,  because  he  found  that  when, 
mixed  in  proportions  of  8,  5,  and  3,  blue,  red,  and  yellow 
make  white,  he  argued  that  the  quantities  of  these  colors 
used  in  the  same  composition  should  represent  these  pro- 
portions. A law  of  this  kind,  however,  though  it  might 
be  applied  to  decoration,  would  evidently  interfere  with 
one  of  the  first  requisites  of  the  art  of  painting,  namely, 
that  it  should  represent  nature.  In  how  many  landscapes 
can  we  find  the  blue  of  the  sky,  or  the  green  of  the  foliage, 
or  the  bluish-gray  of  a lowery  day  exactly  mingled  in 
these  quantities  with  the  warmer  and  lighter  yellows,  reds, 
or  browns  ? Or,  if  now  and  then  a landscape  of  this 
kind  could  be  found,  think  how  greatly  a rule  so  exact 
would  interfere  with  the  freedom  of  the  artist ! 

On  the  face  of  it,  therefore,  this  theory  does  not  seem 
tenable;  and  this  fact  ought  to  be  accepted  as  an  indica- 
tion that,  with  all  the  truth  that  there  is  at  the  basis  of  the 
Field-theory,  it  does  not  contain  the  whole  nor  the  funda- 
mental truth.  What  this  is  may  be  inferred  from  what  was 
said  in  Chapter  XX.  If  we  may  suppose  that  a color  asso- 
ciated with  its  complementary  produces  in  the  eye  an  agree- 
able effect  because  for  the  vibrations  causing  both  colors  as 
well  as  white  light,  or  light  in  general,  there  is  a common 
multiple ; then  we  may  also  suppose  that  these  colors  in- 
fluence, at  the  same  time,  the  organs  of  the  same  retina 

without  producing  any  sensation  of  jolting  or  jarring. 

23 


354 


PROPORTION  AND  HARMONY. 


They  all  seem  to  be  variations  of  the  same  unity  in  that 
they  are  partial  effects  of  the  same  single  impulse  or  set 
of  impulses,  resulting  in  a free,  unconstrained  vibratory 
thrill  or  glow.  The  quantity  of  color,  therefore,  makes 
no  difference  with  the  harmony  of  the  effect.  All  that  is 
necessary  is  that  the  form  of  vibration  causing  the  one 
color,  be  it  much  or  little,  should  exactly  coalesce  with 
the  form  of  vibration  causing  the  other  color. 

This  is  the  same  principle,  explained  physiologically, 
that  those  who  perceive  the  insufficiency  of  the  Field- 
theory  usually  explain  psychologically.  They  say  that 
the  slightest  spot  of  crimson  against  the  green  of  a forest, 
or  of  yellow  against  the  blue  of  the  sky,  is  all  that  is 
needed  in  order  to  bring  out  the  brilliancy  of  the  comple- 
mentary coloring;  and  they  point,  as  an  illustration  of 
this,  to  effects  like  those  in  Jules  Breton’s  picture  entitled 
“ Brittany  Washerwomen,”  at  one  time  in  the  Metropoli- 
tan Museum  of  New  York,  where  a very  little  red  in  the 
bodice  of  the  central  woman  is  enough  to  put  fire  and 
brightness  into  the  pervading  greenish-blue  tints  of  the 
whole.  What  is  thus  said  of  such  arrangements  of  color  is 
true.  But  when  it  is  added  that  these  effects  are  owing 
to  merely  a suggestion  given  to  the  mind,  one  must 
demur.  Those  who  say  it  have  forgotten  a very  import- 
ant principle  in  aesthetics.  This  is,  that  psychological 
effects  (see  “ Art  in  Theory,”  Chapter  XII.)  must  harmon- 
ize with  physiological,  and,  as  the  latter  come  first  in  the 
order  of  time,  especially  when,  as  in  the  present  instance, 
the  effects  have  to  do  primarily  with  form,  it  is  not  logical 
either  to  overlook  them  or  to  fail  to  consider  them  first. 

What  has  been  said  of  the  influence  in  a painting  of 
very  slight  quantities  of  complementary  coloring  will  sug- 
gest a transition  from  the  art-methods  of  comparison,  con- 


TONE. 


355 


trust , and  complement , which  we  have  been  considering  in 
Chapters  XIX.  and  XX.,  to  principality.  (See  the  chart  on 
page  3.)  Of  course  this  method  applied  to  our  present 
subject  would  involve  the  main  use  of  one  color,  to  which 
other  colors  would  be  kept  subordinate.  To  those  ac- 
quainted with  the  terminology  of  painting,  the  mention 
of  this  effect  recalls  that  which  is  ordinarily  treated  under 
the  designation  of  tone.  Tone  is  a term  often  used  as  if  it 
meant  merely  a predominating  or  sometimes  exclusive 
employment  of  one  color  varied  only  by  the  tints  and 
shades  resulting  from  the  effects  of  different  degrees  of 
light.  Thus,  in  a scene  representing  moonlight  or  twi- 
light, or  even  a storm,  especially  if  at  sea,  there  would 
necessarily  be  one  pervading  color,  in  some  cases  banish- 
ing almost  the  suggestion  of  other  colors;  and  such  a 
picture  would  be  said  to  be  particularly  characterized  by 
tone.  The  same  effect  can  also  be  produced  merely 
by  arrangement.  For  instance,  in  the  painting  by  Carl 
Marr  in  the  New  York  Museum  entitled  “ Gossip,”  almost 
every  prominent  object — the  window-curtain,  the  table- 
cloth, the  apron  of  one  of  the  principal  figures,  the  bodice 
of  another,  the  floor,  etc. — -is  depicted  in  white.  On  the 
other  hand,  in  Fortuny’s  “ Spanish  Lady,”  hanging  near  it, 
almost  every  article  of  clothing  is  depicted  in  black  ; while 
in  Granet’s  “ Monks  in  an  Oratory,”  a little  farther  on, 
the  color  of  the  monks’  robes,  as  well  as  of  the  walls  and 
woodwork,  is  all  brown.  Such  paintings  are  said  to  be 
characterized  by  tone , and,  as  this  quality  is  usually  under- 
stood, it  is  difficult  to  perceive  why  it  does  not  fulfil  a 
different  law  of  harmony  from  that  which  is  fulfilled 
through  a use  of  great  variety  in  coloring.  Indeed,  it  is 
often  represented  that  it  does  ; as  if  the  theory  that  har- 
mony of  coloring  is  produced  by  uniformity  of  coloring 


356 


PROPORTION  AND  HARMONY. 


were  antagonistic  to  the  theory  that  it  is  produced  by 
variety. 

But,  by  taking  into  consideration  the  physiological  re- 
quirements of  coloring,  suggested  in  Chapter  XX.,  an 
identical  law  can  be  perceived  to  be  operative  in  both 
cases.  As  shown  on  page  347,  differences  in  tints  and 
shades  of  the  same  hue,  while  they  involve  differences  in 
the  intensity  of  the  sight-waves,  do  not  necessarily  involve 
differences  in  their  rates  or  shapes  of  vibration.  There- 
fore uniformity  of  coloring  is  fitted  to  cause  all  the  vibra- 
tions of  the  same  retina  to  coalesce,  i.  e.,  to  cause  all  to  be 
exact  subdivisions  of  some  common  multiple.  Again,  the 
same  is  true  when  an  effect  of  principality  in  coloring  is 
produced  by  the  use  of  one  predominating  color  with  its 
various  tints  and  shades,  enlivened,  as  in  the  case  of  Jules 
Breton’s  “ Brittany  Washerwomen,”  mentioned  on  page 
354,  by  an  occasional  introduction  of  some  tint  or  shade 
of  its  complementary  color.  The  same  is  true  even 
where  both  complementary  colors  are  used  in  almost 
equal  proportions.  In  fact,  the  same  may  be  true  of 
paintings  characterized  by  the  very  greatest  variety, 
— variety  so  great  that  principality,  while  exerting  a very 
powerful  influence,  can  be  discerned  only  as  a result  of 
much  study. 

To  recognize  how  the  same  physiological  principle,  ful- 
filled in  what  is  termed  tone,  is  really  exemplified  in  all 
cases,  let  us  go  back  again  to  the  analogy  suggested  by 
the  relations  of  notes  in  musical  harmony.  It  will  be 
shown  on  page  397  that  the  colors  of  the  spectrum  repre- 
sent differences  corresponding  to  only  those  of  a single 
octave  in  sound  ; but,  at  the  same  time,  owing  to  the 
minuteness  of  the  color-waves  and  to  the  innumerable 
changes  produced  by  different  degrees  of  light  and  of 


TONE. 


357 


shade  and  of  mixture  with  other  colors,  the  possibilities 
of  variety  in  the  case  of  color  are  much  greater  than  in 
the  case  of  sound.  It  has  already  been  shown  that,  if 
the  forms  of  vibration  produced  by  all  the  adjoining  colors 
are  to  continue  exact  subdivisions  of  one  common  multi- 
ple, every  change  in  one  color,  especially  in  the  degree  of 
the  prominence  of  this  color,  as,  for  instance,  when  it  is 
an  atmospheric  tint  like  the  yellow  of  a sunset  or  the 
gray  of  a twilight,  necessitates  a change  in  every  other 
color  that  is  to  be  used  near  it.  This  is  merely  what  is 
necessary  physiologically  if  the  eye  would  experience  the 
harmonious  effect  of  a thrill  or  glow,  and  not  the  inhar- 
monious effect  of  a series  of  jolts  and  jars. 

The  connection  between  this  principle  and  that  exem- 
plified in  musical  harmony  is  as  follows:  If  we  are  com- 
posing in  the  scale  of  C natural,  we  use  C for  do,  D for 
re,  E for  me,  etc.,  and,  for  the  major  chord,  C,  E,  and  G. 
But  if  we  make  the  slightest  change  in  our  do,  passing, 
for  instance,  into  the  scale  of  D,  then  we  use  D for  do,  E 
for  re,  F sharp  for  me,  etc.,  and,  for  the  major  chord,  D, 
F sharp,  and  A,  these  three  notes  in  the  scale  of  D repre- 
senting exactly  the  same  relationships  between  ratios  of 
vibrations  that  C,  E,  and  G do  in  the  scale  of  C natural. 
There  is  a sense  in  which  it  may  be  said  that  analogous 
changes  are  made  in  color-harmony.  The  only  difference 
is  that  in  music  the  number  of  vibrations  causing  tones  is 
comparatively  few,  and  men  have  been  able  to  calculate 
them,  to  construct  scales  from  them,  and  with  well-nigh 
mathematical  accuracy  to  relate  them  according  to  certain 
ratios.  But  in  color  the  vibrations  are  so  numerous,  and 
the  variations  caused  by  them  so  beyond  calculation,  that 
the  result  is  difficult  to  attain.  Yet  both  cases  illustrate 
apparently  the  same  principle.  When,  in  painting,  we 


353 


PROPORTION  AND  HARMONY. 


change  one  color,  especially  in  the  degree  in  which  it 
is  a prominent  color,  we  change  the  key  of  the  composi- 
tion, and  all  the  colors  need  to  be  keyed  or  toned  into 
harmony  with  this.  Inasmuch,  therefore,  as  the  same 
physiological  conditions  underlie  the  effect,  whether  there 
be  uniformity  or  variety  of  color,  the  same  word  tone  with 
equal  appropriateness  might  be,  though  it  is  not,  applied 
in  all  cases. 

What  has  been  said  will  explain  sufficiently  the  rela- 
tionship to  effects  of  harmony  of  principality  and  its  neces- 
sary accompaniment,  subordination.  The  next  method 
in  the  chart  on  page  3 is  balance.  This  is  the  method  that 
leads,  in  music  or  poetry,  sometimes  to  repetition,  and 
sometimes  to  alternation  on  upward,  or  downward,  or  long 
or  short  movements  in  phrases,  lines,  or  rhymes  ; and  that 
leads,  in  painting,  sculpture,  or  architecture,  to  likeness  in 
whole  or  part  on  opposite  sides,  as  in  eyes,  ears,  arms,  or 
wings  of  living  creatures  or  buildings.  As  brought  out  at 
length  in  Chapters  III.  to  V.  of  “ The  Genesis  of  Art- 
Form,”  balance  is  necessary  in  order  to  convey,  in  con- 
nection with  principality  and  subordination , the  impression 
of  organic  form , the  next  method  mentioned  in  the  chart 
on  page  3.  The  same  must  be  true,  of  course,  as  applied 
to  the  arrangements  of  color.  We  gain  an  impression  of 
unity  or  organism  of  form  in  a composition,  considered  as 
a whole,  in  the  degree  in  which,  through  a use  of  light  and 
shade  or  hue,  the  sides  are  balanced,  as  we  say.  Thus,  in 
Rubens’s  well  known  “ Descent  from  the  Cross,”  Fig.  129, 
page  359,  a white  sheet,  the  whitest  object  in  the  picture, 
is  placed  behind  the  form  of  the  Christ  ; but  on  both 
sides  of  this  the  light  is  reflected  from  surrounding  faces 
or  forms,  and  is  so  disposed  that  all  of  it  that  is  on  one 
side  is  carefully  balanced  by  that  which  is  on  the  other 


FIG.  129.— “THE  DESCENT  FROM  THE  CROSS,”  BY  RUBENS. 
See  pages  59,  303,  358,  363,  365,  367,  369. 


359 


360  PROPORTION  AND  HARMONY. 

side,  a dish  and  parchment  at  the  lower  right  corner  be- 
ing especially  prominent,  as  balancing  the  light  from  the 
shoulders  of  a man  at  the  upper  left  corner. 

The  impressions  of  balance  and  of  organic  form,  as  thus 
produced,  point  toward  a psychical  rather  than  a physio- 
logical explanation.  It  is  the  mind,  not  the  visual  appa- 
ratus, that  is  satisfied  by  such  a use  of  color.  And  yet 
we  might  mistake,  did  we  suppose  that  from  these  effects 
physiological  influences  were  wholly  absent.  It  is  impos- 
sible for  the  eyes  to  look  at  a picture  without  almost  con- 
stantly shifting  the  gaze  from  one  side  of  it  to  the  other 
side.  If,  while  doing  so,  they  perceive  exactly  the  same 
color  on  both  sides,  they  will  notice  this  color  particularly. 
While  doing  so,  moreover,  the  retina  will  experience  no 
perceptible  difference  or  change  in  the  character  of  its 
vibrations,  and,  therefore,  as  explained  on  page  350,  it 
will  experience  nothing  interfering  with  the  requirement 
of  harmony.  This  physiological  fact  will  explain  why,  in 
order  to  convey  an  impression  of  balance,  equal  quantities 
of  color  on  both  sides  of  a picture  are  not  necessary. 
Things  that  harmonize  with  a third  thing,  harmonize 
with  one  another.  A iittle  color  on  one  side,  harmon- 
izing with  its  surroundings,  will  harmonize  with  a great 
deal  of  this  same  color  on  the  opposite  side.  In  accord- 
ance with  this  principle,  in  one  of  Paul  Veronese’s  pic- 
tures— he  painted  more  than  one — of  the  “ Marriage  at 
Cana,”  a small  black  dog  on  one  side  is  said  to  balance  a 
large  mass  of  black  upon  the  other  side;  and  in  Jules 
Breton’s  “ Brittany  Washerwomen,”  mentioned  on  page 
354,  a little  blue  in  certain  of  the  women’s  skirts  balances 
a much  larger  amount  of  blue  in  a sea  on  the  opposite 
side  of  the  picture.  The  same  fact  explains,  too,  why  a 
color  on  one  side  is  often  represented  as  balancing  (though 


BALANCE. 


361 

this  is  not  an  exact  use  of  the  term ; see  the  chart  on 
page  3)  on  the  other  side  not  the  same  color  but  its  com- 
plementary. It  is  said  to  balance,  of  course,  because  the 
vibrations  occasioning  a color  harmonize  with  those  occa- 
sioning its  complementary,  as  well  as  with  those  occasion- 
ing its  own  color.  In  a like  way,  one  can  explain  the 
effect  of  an  arrangement  in  Henri  Lerolle’s  “Organ  Re- 
cital” in  the  Metropolitan  Museum,  New  York,  whereby 
all  the  darker  tones  are  in  the  shade  at  the  left  lower  side 
of  the  picture,  and  all  the  bright  tones  are  in  the  light  at 
the  right  upper  side ; the  two  classes  of  tones  in  this  case 
being  about  evenly  divided. 

The  general  impression  produced  by  balance  enters 
largely  as  we  shall  find  presently,  into  the  effects,  which 
are  all,  in  fact,  developments  of  it,  termed  parallelism,  al- 
ternation, symmetry,  and  continuity.  But  before  consider- 
ing these,  following  the  order  of  the  art-methods,  as 
indicated  in  the  chart  on  page  3,  let  us  take  up  for  a mo- 
ment that  phase  of  comparison  which  is  termed  congruity. 
This  is  the  principle  which  causes  all  factors,  including 
color,  to  be  selected  not  so  much  because  they  are  alike 
in  form,  as  because  they  represent  like  conceptions  or 
conditions.  See  Chapter  XI.  of  “ Painting,  Sculpture,  and 
Architecture  as  Representative  Arts.”  The  degree  of  im- 
portance that  should  be  attached  to  the  representation 
of  like  conceptions  in  the  forms  that  are  grouped  together, 
is  difficult  for  some  to  recognize.  Yet  if,  as  was  said  on 
page  344,  the  difference  between  the  effects  of  harmony 
and  of  discord  be  the  difference  between  experiencing  in 
the  nerves  an  unimpeded,  free,  regularly  recurrent  vibra- 
tory thrill  or  glow,  and  experiencing  an  impeded,  con- 
strained, irregularly  recurrent  series  of  shocks  or  jars,  then 
an  application  of  the  simplest  physiological  principles 


362 


PROPORTION  AND  HARMONY. 


ought  to  show  us  that  the  artistic  effects  of  which  we  have 
spoken  can  be  produced  in  part  by  the  representation  of 
like  conceptions.  It  is  universally  admitted  that  the 
nerves,  merely  as  nerves,  may  be  affected  from  the 
thought-side  as  well  as  from  the  sense-side.  Whatever, 
therefore,  owing  to  incongruity  between  thought  and  form 
or  between  different  thoughts  as  represented  by  different 
forms,  shocks  one’s  conceptions  or,  as  we  say,  one’s  sense 
of  the  proprieties,  may  so  contribute  to  the  general  nervous 
result  that,  even  though  he  may  find  the  combinations  of 
color  thoroughly  pleasing,  it  is  physiologically  impossible 
that  he  should  experience  the  effects  of  beauty  in  its  to- 
tality. On  this  subject  the  reader  may  consult  Chapter 
XIII.  of  “Art  and  Theory.” 

A moment’s  thought  will  reveal,  too,  that  having  the 
colors  represent  like  conceptions  or  conditions  is  often 
the  most  effective  way  in  which  to  have  them  represent 
likeness  in  hue.  According  to  the  principles  unfolded 
on  page  314,  gaslight,  firelight,  twilight,  moonlight,  cloud- 
light,  and  even  sunlight,  at  certain  times  of  the  day, 
develop  their  own  colors  so  far  as  they  are  found  in  sur- 
rounding objects,  and  cause  these  colors  to  be  reflected 
from  all  other  objects  in  the  degree  in  which  their  surfaces 
are  of  a glossy  kind  of  white,  or,  to  use  an  unscientific 
term,  are  glass-like.  If  a painter  wish,  therefore,  to  have 
his  work  as  a whole  convey  a general  impression  of  cheer- 
fulness or  of  gloom,  the  most  effective  way  in  which  he 
can  make  it  do  this  is  to  make  it  fulfil  the  method  of  com- 
parison by  way  of  congruity. 

The  modifications  of  congruity  under  the  influence  of 
variety  and  complexity  causing  the  effects  of  incongruity 
and  comprehensiveness , it  is  not  necessary  to  explain. 
Everybody  knows  that  the  mere  fact  that  a painting  is  a 


ELEMENTS  OF  COLOR-HARMONY. 


363 


picture  of  some  actual  scene,  often  necessitates  the  intro- 
duction of  incongruous  hues,  and  that  these  can  only  be 
harmonized  by  the  addition  of  other  hues  complementing 
or  connecting  them,  and  thus  causing  more  or  less  compre- 
hensiveness of  effect.  See  what  is  said  on  page  364  of  K.  G. 
Hellquist's“  Sonnanvater  and  Knut  Entering  Stockholm.” 
A few  words,  too,  will  express  all  that  is  necessary  with 
reference  to  the  influence  upon  colors  of  the  art-methods 
in  the  chart  on  page  3 termed  central-point  (or  radiation ), 
setting , and  parallelism.  Recalling  that  all  these  are 
methods  of  producing  effects  of  unity  in  a composition 
considered  as  a whole,  it  will  be  noticed  that  radiation , 
though  usually  associated  in  our  minds  with  the  idea  of 
very  distinct  outlines,  does  not  necessarily  involve  these. 
For  instance,  in  Fig.  38,  page  75,  as  also  in  Fig.  129,  page 
359,  there  is  a very  decided  effect  of  centring  and,  by 
consequence,  of  unity  as  produced  by  it,  but,  in  Fig.  129, 
it  is  by  the  colors  rather  than  by  the  lines  that  the  effect 
is  brought  out. 

Setting , as  applied  to  color,  is  mainly  an  arrangement 
within  a framework  of  organic  form , when  characterized 
by  central-point  or  parallelism , or  both,  whereby,  in  accord- 
ance with  the  laws  of  consonatice,  to  be  considered  pres- 
ently, the  degree  of  light  illumining  an  object,  or  the 
peculiarity  of  hue  characterizing  it,  causes  its  outlines  to 
appear  not  only  distinct  and  different  but  aesthetically 
effective.  Parallelism , like  radiation , is  usually  associated 
with  the  conception  of  lines;  but  in  all  cases  these  may 
be  merely  suggested  by  the  colors,  as  when,  for  instance, 
we  see  a blue  lake  with  a ridge  of  mountains  behind 
them,  and  a blue  sky  perhaps  above  the  mountains;  or  a 
river  or  ledge  of  rocks  separating  a line  of  green  foliage  in 
the  foreground  from  a line  of  green  forest  a little  farther 


364 


PROPORTION  AND  HARMONY. 


back.  Nor  is  the  effect  of  parallelism  through  the  use  of 
complementary  colors  uncommon.  How  often  we  see  a 
stretch  of  blue  sky  above  a like  stretch  of  yellow  sand,  or 
vice  versa , ruddy  or  golden  layers  of  sunset  clouds  lying 
above  the  greenish  or  bluish  tints  of  grass  or  waves  be- 
neath them. 

Symmetry  involves  the  principle  of  balance  applied  to 
arrangements  not  on  two  sides,  but  on  every  side  of  a 
common  centre.  There  is  an  illustration  of  this  effect  in 
the  “Thusnelda  at  the  Triumph  of  Germanicus,”  by  Karl 
Piloty  in  the  Metropolitan  Museum.  In  this  picture, 
with  sufficient  variety  not  to  obtrude  itself  so  as  to  seem 
unnatural,  the  color,  whether  light  or  dark,  that  is  above 
or  below  or  in  one  corner,  is  almost  invariably  balanced 
by  a mass  of  the  same  color  in  very  nearly  the  same  po- 
sition below  or  above  or  in  the  opposite  corner.  A more 
unusual  illustration  of  this  kind  of  arrangement,  the  in- 
fluence of  which,  because  not  connected  with  much  massing 
of  light  or  shade,  tends  principally  to  a general  picturesque- 
ness of  effect,  is  afforded  in  a painting  that  hangs  near 
this  in  the  same  gallery,  i.  e .,  K.  G.  Hellquist’s  “ Sonnan- 
vater  and  Knut  Entering  Stockholm.”  Here  the  legs 
of  three  of  the  figures,  one  in  the  middle  and  one  on  each 
side,  are  clad  in  the  same  shade  of  brown.  A clown’s 
coat  on  one  side,  a horse’s  tail  on  the  other,  and  the  legs 
of  a figure  in  the  centre  are  all  in  the  same  shade  of  yel- 
low. A woman’s  cap  on  one  side,  a man’s  coat  on  the 
other,  and  a woman’s  dress  far  above  these,  all  show  the 
same  shade  of  blue  ; while  a bright  red  cap  on  one  side 
balances  a bright  red  cap  on  the  other,  and  the  same  is 
true  of  a dark  red  cap  as  related  to  a dark  red  cape. 

Repetition  of  form  involves,  in  some  regards,  the  most 
easy,  because  the  most  elementary  way  of  putting  like 


REPETITION. 


365 


with  like  according  to  the  art-method  of  comparison. 
Notice  the  outlines,  in  Figs.  38,  page  75,  and  129,  page 
359.  But  the  same  fact  is  also  true  as  applied  to  colors. 
This  is  one  reason  why  pictures  characterized  by  tone , as 
its  meaning  is  limited  on  page  355,  are  apt  to  be  more 
satisfactory  than  those  characterized  by  great  diversity  of 
coloring.  These  latter,  notwithstanding  the  success  of 
some  brilliant  colorists  like  Fortuny,  Zamagois,  Rico,  and 
others  of  the  Spanish-Roman  school,  are  usually  avoided 
by  wise  artists.  As  Van  Dyke  says  in  his  “ Flow  to  Judge 
of  a Picture”:  “Beware  of  bright  pictures,  for  they  are 
generally  bad.  . . . Look  at  the  grays  and  browns ; 

the  low-toned  and  half-tinted  pictures — look  at  them,  not 
once  only,  but  several  times,  for  there  is  likely  to  be 
something  in  them  that  you  do  not  see  at  first  glance.” 
It  must  not  be  thought,  however,  that  these  latter  pic- 
tures, though  involving  _^wer  difficulties  in  the  way  of 
securing  unity  of  color-effect,  do  not  involve  other  great 
difficulties.  In  cases  where  the  color  is  almost  absolutely 
the  same  throughout,  it  is  no  easy  matter  to  represent 
different  degrees  of  light  and  shade.  Nor  must  it  be 
supposed  that  pictures  without  diversity  of  coloring  can 
always  be  made  true  to  nature.  In  full  sunshine,  or  in 
full  light  of  any  kind,  in  which  the  shadows  are  deep  and 
the  colors  are  brilliant,  they  are  almost  necessarily  greatly 
varied.  Even  then,  however,  whether  an  artist  take  sun- 
set in  a land  robed  in  the  full  glories  of  autumn  foliage, 
or  firelight  in  a room  papered  and  upholstered  in  red,  or 
a scene  less  harmoniously  toned  by  nature,  it  is  evident 
that,  in  spite  of  great  brilliancy  of  coloring,  he  can  produce 
unity  of  effect  through  repetition.  At  the  same  time,  we 
are  more  accustomed  to  repetition  when  the  colors  are 
not  bright ; and,  therefore,  it  seems  more  natural  when 


366 


PROPORTION  AND  HARMONY. 


the  impression  conveyed  is  that  of  weirdness  and  mystery, 
as  indicated  by  twilight  or  moonlight,  or  of  gloom  or 
ruin,  as  indicated  by  a lowery  or  stormy  atmosphere, 
which  gives  everything  in  cloud  and  earth  a tinge  of  gray. 

Alteration,  the  next  method  in  the  chart  on  page  3,  is 
merely  a phase  of  variety  in  connection  with  repetition, 
and  alterjiation  a phase  of  balance  by  means  of  contrast. 
Piloty’s  “ Thusnelda  at  the  Triumph  of  Germanicus,”  and 
Hellquist’s  “ Sonnanvater  and  Knut  Entering  Stock- 
holm,” mentioned  on  page  364,  furnish  illustrations  of 
both  of  these  as  well  as  of  symmetry. 

Next  to  alternation,  and  closely  connected  with  both 
principality  and  central-point,  is  massing.  This  word,  as 
applied  to  the  use  of  crayon  or  pigments — and  by  some  it 
is  applied  to  these  almost  exclusively — refers  to  those 
effects  of  light  and  shade  in  ''''mnection  with  color  whereby 
bright  features  are  put  with  Dnght,  and  dark  with  dark. 
As  a result  of  such  arrangements,  a breadth  of  distance 
seems  to  separate  the  objects  in  light  from  those  in  shade, 
and  a corresponding  breadth  of  view  seems  to  be  afforded 
him  who  sees  them  ; hence  the  term  breadth  is  sometimes 
used  interchangeably  with  massing.  In  securing  this  effect 
the  artist  does  not  arbitrarily  make  objects  bright  or  dim 
in  order  to  have  them  correspond  to  the  bright  or  dim 
parts  of  the  picture  in  which  he  wishes  to  place  them. 
He  exercises  ingenuity  in  arranging  his  materials  so  as  to 
bring  into  the  right  relations  objects  that  in  nature  are 
bright  or  dim,  or  that  can  be  made  so  in  nature  by  the 
presence  or  absence  of  an  illuminating  agent.  Besides 
this,  too,  he  arranges  the  light  so  as  to  fall  where  it  will 
prove  most  effective.  In  Titian’s  “ Entombment,”  it  is 
made  to  illumine  a figure  in  the  foreground,  notwith- 
standing the  fact  that  the  sun  is  represented  as  setting  in 


MASSING. 


367 


the  background.  The  painter  produces  the  effect  by  sup- 
posing the  sun’s  rays  to  be  reflected  from  a cloud  in  ad- 
vance of  the  field  of  vision.  Notice  also  the  way  in  which 
the  light  is  massed  in  Rubens’s  “ Descent  from  the  Cross  ” 
(Fig.  129,  page  359). 

It  is  not  to  be  supposed,  however,  that  in  any  given 
picture  there  may  not  be  more  than  one  place  where  there 
is  light  and  one  place  where  there  are  shadows,  although 
in  the  paintings  of  Correggio  and  Rembrandt,  who  de- 
veloped most  fully  the  possibilities  of  light  and  shade,  or 
of  chiaroscuro,  as  it  is  called,  this  plan  was  usually  fol- 
lowed. According  to  Reynolds  (Note  xxxix.  on  “ The 
Art  of  Painting”),  there  may  be  three  masses  of  light, 
one  of  which,  however,  he  would  make  more  prominent 
than  the  other  two,  thus  causing  all  three  together  to  ful- 
fil the  methods  both  of  principality  and  of  balance.  Titian, 
in  order  to  impress  the  fact  that  every  picture  represent- 
ing the  effects  of  the  atmosphere  must  indicate  not  only 
the  general  influence  of  the  light  and  shade  on  all  the  ob- 
jects depicted  considered  together,  but  on  each  specific 
object  considered  by  itself,  is  said  to  have  pointed  to  a 
bunch  of  grapes,  and  shown  how  the  bunch  considered 
as  a whole  has  a light  and  a dark  side,  and  also  how  each 
grape  considered  by  itself  has  a light  and  a dark  side. 
The  effects  resulting  from  each  of  these  conditions  render 
the  representation  of  both  difficult.  Nor  can  they  be  rep- 
resented at  all  except  in  the  degree  in  which  the  general 
effect,  which  is  the  one  connected  with  massing,  is  treated 
as  the  more  important  of  the  two. 

From  what  has  been  said,  it  is  evident  that  the  effect 
of  breadth,  as  thus  produced,  is  identical  with  that  of  the 
accumulation  of  repeated  characteristics  which  results 
from  massing  in  poetry  and  music.  The  artistic  end  in 


368 


PROPORTION  AND  HARMONY. 


view,  too,  is  the  same.  By  it,  the  unity , comparison , prin- 
cipality, congruity,  central-point , as  well  as  repetition  of 
the  product  are  all  brought  out  more  clearly.  “ Pictures,” 
says  S.  P.  Long  in  his  “ Art,  Its  Laws,  and  the  Reasons 
for  Them,”  essay  vi. — “ Pictures  possessing  breadth  of 
the  general  light  and  dark  or  shade  are  not  only  very 
effective,  but  they  likewise  give  great  repose  to  the  eye  ; 
whereas,  where  the  lights  and  darks  are  in  small  portions, 
and  much  divided,  the  eye  is  disturbed  and  the  mind 
rendered  uneasy,  especially  if  one  is  anxious  to  under- 
stand every  object  in  a composition,  as  it  is  painful  to  the 
ear,  if  we  are  anxious  to  hear  what  is  said  in  company, 
where  many  are  talking  at  the  same  time.  Hence  . . . 
the  reason  why  portraits  make  a more  pleasing  picture 
when  but  few  objects  are  introduced  into  the  composi- 
tion than  when  the  person  is  covered  with  frills  and 
ruffles,  and  the  background  stuffed  like  a ‘ curiosity  shop.’ 
Such  an  arrangement  cuts  up  the  lights  and  darks  and 
destroys  the  breadth” — a statement  applicable,  as  will  be 
noticed,  not  only  to  massing  but  also  to  interspersion , its 
opposite,  according  to  the  chart  on  page  3.  Concerning 
the  same  subject  Ruskin  says  in  his  “ Elements  of  Draw- 
ing,” letter  iii. : “ Such  compositions  possess  higher  sub- 
limity than  those  which  are  more  mingled  in  their 
elements.  They  tell  a special  tale  and  summon  a definite 
state  of  feeling.  We  have  not  in  each  gray  color  set 
against  sombre,  and  sharp  forms  against  sharp,  and  low 
passages  against  low ; but  we  have  the  bright  picture 
with  its  single  ray  of  relief ; the  stern  picture  with  only 
one  tender  group  of  lines;  the  soft  and  calm  picture  with 
only  one  rock  angle  at  its  flank,  and  so  on.” 

When  there  is  no  massing  of  color,  and  the  lights  and 
darks  are  mingled  indiscriminately,  there  is  little  unity. 


MASSING. 


369 


Instead  of  it  we  have  that  phase  of  variety  termed,  in 
“The  Genesis  of  Art-Form,”  interspersion.  When,  in 
spite  of  apparent  interspersion,  there  is  massing,  methodi- 
cally distributed  too,  but  apparently  alternating  in  differ- 
ent places,  as  where  the  light  falls  through  branches  of 
trees  or  lattice-work,  we  have  the  picturesque  equivalent 
in  color  of  artistic  complication.  Notice  again  what  is 
said  on  page  364  of  Hellquist’s  “ Sonnanvater  and  Knut 
Entering  Stockholm.”  Once  more,  when,  notwithstand- 
ing this  form  of  alternation,  we  have,  as  in  a sunset  sky,  or 
in  views  of  rivers,  seas,  mountains,  forests,  similar  coloring 
not  merely  continuous  but,  if  interrupted,  caught  up  and 
continued,  so  as  to  convey  an  unmistakable  unity  of  im- 
pression, as  if  all  the  other  colors  were  set  into  its  flexible 
framework,  then,  though  continuity  as  well  as  complication 
are  words  borrowed  from  the  relationships  of  lines,  we 
may  say  that  we  have  examples  of  the  effects  in  coloring 
of  both  of  these  methods.  See  the  general  lines,  though 
in  these  illustrations  necessarily  indicated  only  by  light 
and  shade,  in  Figs.  38,  page  75  ; 75,  page  142 ; 102,  page 

235  ; and  129,  page  359. 

24 


CHAPTER  XXII. 


SPECIAL  EFFECTS  OF  COLORS  WHEN  PLACED  SIDE  BY  SIDE. 

Consonance — Importance  of  this  Subject — Colors  Placed  Side  by  Side  Pro- 
duce Subjective  Effects  in  the  Eye- — Successive  Contrast  or  After- 
Image  of  Complementary  Colors  Following  Colors  Suddenly  Obscured 
— A Similar  Phenomenon  among  Sounds — Explanation  of  Differences 
between  the  Phenomena — Ordinary  Explanation  of  the  After-Images — 
Simultaneous  Contrasts  asin  Shadows — Suggested  Insufficiency  of  Rea- 
sons Ordinarily  Given  for  Successive  and  Simultaneous  Contrast — 
Suggestions  with  Reference  to  the  Perception  of  Color — Nothing  in 
the  Organism  to  Throw  Doubt  upon  these  Suggestions — The  Principle 
Involved  Explains  the  Main  Difference  between  Successive  and  Simul- 
taneous Contrast— Colors  Impart  about  them  Tints  of  their  Comple- 
mentaries — These  Effects  on  Light  and  Shade  or  on  Light  and  Dark 
Neutral  Surfaces  as  Produced  by  Warm  and  Cold  Colors — By  Different 
Tints  and  Shades — Same  Effects  as  Produced  on  Colored  Surfaces — 
Three  Ways  of  Using  Contrast  to  Relieve  Objects  from  their  Back- 
ground. 


ONSONANCE,  the  next  art-method  in  the  chart  on 


page  3,  is  the  element  causing  factors  to  be  put  to- 
gether by  way  of  comparison  because  they  are  alike  in 
formative  principles.  How  the  theory  is  tenable  that 
colors  may  differ  and  yet  result  from  forms  of  vibrations 
having  a common  multiple,  and  all  therefore  coalescing 
and  producing  in  the  eye  the  sensation  of  an  absolutely 
free,  unimpeded,  regularly  recurrent  vibratory  thrill  or 
glow,  is  suggested  in  Chapter  XX.  It  is  a further  devel- 
opment of  this  suggestion  to  which  attention  will  be 
directed  in  the  present  chapter. 

On  page  351,  it  was  said  that  the  art-methods  which,  in 


370 


SUBJECTIVE  COLOR-EFFECTS. 


371 


the  chart  on  page  3,  precede  consonance , and  which  we 
have  now  considered,  determine  the  selection  and  ar- 
rangement of  colors  with  reference,  mainly,  to  their  gen- 
eral effects  in  a painting  considered  as  a whole  ; whereas 
consonance  and  the  methods  following  it  have  to  do  main- 
ly with  the  special  effects  of  the  colors  when  placed 
side  by  side.  It  may  be  said  now,  that,  of  all  the 
methods,  these  latter  are  the  most  important  because  the 
most  fundamental.  In  music,  it  is  absolutely  essential 
that  all  the  tones  sounded  simultaneously  as  in  chords,  or 
in  immediate  succession,  should  fulfil  certain  physical  and 
physiological  requirements.  If  they  do  not,  all  the  other 
art-methods,  however  scrupulously  applied,  cannot  secure 
harmony.  That  the  same  is  true  with  reference  to  the 
colors  used  side  by  side  or  one  after  another  in  the  order 
of  space  is  a fact  which,  even  if  not  confirmed  by  our  own 
observation,  the  investigations  of  science  would  have 
placed  beyond  dispute. 

It  was  mentioned  on  page  332  that  lines  of  vermilion 
drawn  on  an  ultramarine  ground,  in  other  words,  that  ver- 
milion and  ultramarine  in  juxtaposition,  produce  in  the 
eye  the  effect  of  purple.  All  colors  placed  side  by  side 
give  rise  to  similar  subjective  effects.  Under  conditions 
favorable  to  such  results,  they  may  increase  and  diminish 
each  other’s  brightness,  change  each  other’s  hues,  and 
even  cause  new  colors  in  places  where  there  are  none. 

The  best  way  in  which  to  come  to  recognize  the  full 
bearing  of  this  fact,  is  to  begin  by  studying,  for  a little, 
the  phenomena  respectively  termed  consecutive  and  sim- 
ultaneous contrast.  With  the  first  of  these  we  may 
become  acquainted  thus : If,  after  looking  steadily  for 
a few  seconds  at  a white  wafer  on  a black  ground,  we 
turn  our  eyes  to  a white  or  gray  ground,  with  nothing  on 


372 


PROPORTION  AND  HARMONY. 


it,  we  often  seem  to  see,  nevertheless,  a black  after-image, 
as  it  is  called,  of  the  same  shape  as  the  wafer.  If  we  look 
in  the  same  way  at  a bluish-green  wafer,  and  then  turn 
our  eyes  to  the  gray  ground,  we  often  find  on  it  an  after- 
image of  red,  i.  e.,  of  the  color  which  complements  the 
bluish-green.  So,  if  we  try  other  colors,  as  a rule  we 
find  their  complementary  colors  in  the  after-images.  If, 
when  we  turn  our  eyes  away  from  the  wafer,  the  sur- 
face at  which  we  look  be  of  the  same  color  as  the  wafer, 
the  complementary  color  in  the  after-image  is  pale  and 
faint ; if  the  surface  be  of  the  color  complementary  to 
that  of  the  wafer,  the  complementary  after-image  is  more 
brilliant  than  its  own  color  which  forms  the  background. 
If  the  surface  be  of  any  other  color,  the  complementary 
color  of  the  after-image  blends  with  it  and  produces  a new 
mixed  color.  In  this  way  the  after-image  of  the  bluish- 
green  wafer  would  be  red  on  a white  surface,  faint  red 
on  a bluish-green,  brilliant  red  on  a red,  violet  (z.  e., 
mixed  with  blue)  on  a blue,  orange  (z.  e.,  red  mixed  with 
yellow)  on  a yellow,  and  so  on. 

Before  attempting  an  explanation  of  this  phenomenon, 
it  is  well  to  notice  a correspondence  between  it  and 
an  effect  produced  in  connection  with  musical  tones. 
If  we  hold  down  the  key  of  a piano,  which  if  struck 
would  sound  g, — and  the  same  would  be  true  were  we  to 
hold  down  keys  sounding  one  or  two  other  of  the  lower 
partial  tones  of  Cr,  as  indicated  in  the  music  on  page  341, 
— and  then  strike  violently  the  key  of  the  lower  bass  C', 
lifting  our  finger  instantly  so  as  to  cause  the  hammer 
to  press  against  the  string  and  check  its  sound,  we  shall 
in  most  cases  hear  a sound,  but  it  will  be  that  of  the  string 
the  key  of  which  we  are  holding  down,  and  which  there- 
fore we  have  left  free  to  vibrate.  In  other  words,  we 


SUBJEC  TI VE  SO  UND-EFFE  C TS. 


373 


produce  one  sound  and,  when  its  tone  is  checked,  we 
hear  not  it  but  another  with  which  it  is  in  harmony,  as  is 
said.  What  is  it  that  produces  this  other  sound  ? Evi- 
dently the  string  left  free  to  vibrate,  because  its  tone 
is  the  only  sound  that  we  hear.  But  what  has  caused  this 
string  to  vibrate  ? A sound-wave,  of  course.  But  a sound- 
wave— as  proved  by  experiments  with  tuning-forks  which 
produce  no  partial  tones,  and  therefore  never  respond 
except  to  waves  produced  by  a tone  of  their  own  pitch, — 
causes  no  string  to  vibrate  except  a string  keyed  to 
respond  to  a form  of  wave  that  exists  in  its  own  form. 
Therefore  it  is  argued  that  the  sound-wave  caused  by  the 
string  struck  must  have  been  compounded  ; and  have  con- 
tained, as  one  of  its  constituent  elements,  a sound-wave 
fitted  to  influence  sympathetically  the  string  sounding. 
This  is  the  theory  now  universally  adopted,  especially  as 
it  is  found  that  only  certain  strings  will  sound  thus,  and 
that  these  are  invariably  strings  producing  tones  that  are 
in  harmony  with  the  tone  of  the  string  struck.  But 
notice,  now,  that  that  which  causes  the  vibrations  of  the 
string  that  sounds,  is  not  the  string  itself,  which  is  only  a 
means,  but  the  sound-wave.  Why,  then,  could  not  the 
wave  without  other  strings  cause  other  sounds  ? It  cer- 
tainly could.  Faint  accompanying  tones,  and  even  after- 
tones, are  sometimes  clearly  distinguishable  in  the  main 
tones  of  certain  instruments,  like  violins  and  bugles. 
They  are  usually  heard  ringing  very  distinctly  after  the 
main  tones  of  church  bells  and  low-pitched  steam  whistles, 
while,  as  shown  on  page  225  of  “ Rhythm  and  Harmony 
in  Poetry  and  Music,”  bass  notes  are  sometimes  heard  in 
connection  with  chords  containing  two  notes,  both  com- 
paratively high.  Now,  in  such  cases,  what  are  we  to 
consider  the  results, — as  always  objective  ? No  ; as  some- 


374 


PROPORTION  AND  HARMONY. 


times  subjective,  in  just  as  true  a sense  as  in  the  case  of 
the  after-image  produced  in  the  eye  according  to  the 
method  described  in  the  last  paragraph.  This  much  for 
those  who  claim,  as  some  do,  that  the  phenomena  of 
sound  are  objective,  and  those  of  color  subjective,  and 
therefore  cannot  be  treated  as  analogous. 

It  is  true  that  in  the  case  of  sounds  we  may  hear  not 
merely  one  harmonic  over-tone  or  under-tone,  but  some- 
times others,  while  we  can  never  see  more  than  one 
complementary  color.  But  the  limitation  in  the  realm  of 
sight  has  a cause.  The  numbers  of  vibrations  in  musical 
tones  are  doubled  six  or  seven  times  in  order  to  produce  the 
six  or  seven  octaves  or  scales  ordinarily  used  ; whereas  the 
numbers  of  the  vibrations  causing  the  colors  are  never 
doubled, — for  one  reason,  probably,  because,  owing  to 
their  minute  dimensions,  trillions  of  them  being  produced 
in  a single  second,  all  variations  needed  in  them  can  be 
produced  without  their  being  doubled. 

There  is  nothing,  therefore,  among  the  colors  to  corre- 
spond to  different  octaves.  All  possible  hues  can  be 
represented  within  the  limits  of  a single  octave.  It  is  true 
that  the  terms  high  and  low  are  often  applied,  respectively, 
to  bright  and  dull  shades  or  tints  of  the  same  hue;  and 
this  fact  is  often  supposed  to  warrant  an  analogy  between 
high  and  low  scales  in  music.  But  the  analogy  is  justified 
only  in  the  sense  in  which  the  key  of  C sharp,  because  this 
note  is  half  a tone  higher  than  C natural,  is  higher  than 
the  key  of  C natural.  Between  red  and  orange  there  is 
not,  as  between  C and  D in  music,  a single  interval,  like  C 
sharp,  that  can  be  used,  but  trillions  of  intervals,  any  one 
of  which  may  be  chosen,  as  one  might  say,  for  the  key- 
tone  of  a different  color-scale.  While,  therefore,  there  is 
an  analogy  between  high  tones  and  high  colors,  we  must 


AFTER-IMAGES. 


375 


not  suppose  that  it  involves  the  existence  among  the 
colors  of  any  such  relationships  as  exist  in  music  between 
scales  a full  octave  apart.  With  this  in  mind,  notice  the 
music  on  page  341.  It  represents  notes  that  are  caused  by 
vibrations  respectively  two,  three,  four,  five,  six,  seven, 
eight,  nine,  and  ten  times  as  rapid  as  those  causing  the 
lower  C,  F,  or  G,  immediately  below  them.  These  are 
the  notes  among  which  alone  can  be  found,  owing  to  the 
law  mentioned  on  page  340,  the  after-tones  which  we  are 
now  considering.  But  notice  that  in  the  lowest  octave 
in  which  any  note  except  C appears,  there  is  only  one 
note,  G or  g.  This,  therefore,  is  the  partial  tone,  whose 
relation  to  the  prime  tone  most  fitly  represents  the 
nearest  relationship  that  can  exist  between  harmonic 
colors.  Such  being  the  case,  it  is  worth  observing  that 
the  ratio  between  the  vibrations  causing  a C and  a G, 
when  both  are  in  the  same  octave,  is,  so  far  as  can  be  made 
out,  very  nearly  if  not  exactly  the  same  as  the  ratio  be- 
tween the  vibrations  causing  any  given  color  and  causing 
the  color  most  nearly  corresponding  to  that  which,  when 
produced  in  the  spectrum,  is  termed  its  complementary. 
For  the  proof  of  this,  see  page  401. 

It  is  not  usually  argued  that  these  apparent  corre- 
spondences result  from  any  actual  correspondence  be- 
tween the  actions  of  the  organs  of  sight  and  of  hearing. 
The  explanation  for  after-images  that  is  most  often  con- 
sidered satisfactory,  is  that  certain  of  the  possibilities  of 
energy,  or  certain  organs  in  the  eye,  which  alone  are 
sensitive  to  the  color  of  the  wafer  held  before  it,  as 
indicated  on  page  371,  have  become  fatigued  by  looking  at 
this,  and  have  thus  been  made  insensible  to  the  general 
effects  of  the  light,  whereas  all  the  other  possibilities  or 
organs,  meantime,  have  been  rested.  Accordingly,  when 


376 


PROPORTION  AND  HARMONY. 


the  eye  turns  where  white  light  takes  the  place  of  the  color 
of  the  wafer,  all  the  other  ingredients  of  this  light  affect  it 
before  that  one  which  has  been  seen  in  the  wafer.  All  these 
other  ingredients,  as  we  know,  produce  the  color  comple- 
mentary to  that  of  the  wafer.  Therefore  when  we  look 
away  from  the  wafer’s  color,  we  see  its  complementary. 

As  we  shall  find  presently,  this  theory  probably  con- 
tains a glimmer  of  truth.  But  that  much  more  is  needed 
in  order  to  make  it  a satisfactory  explanation,  will  appear 
when,  from  successive  contrast,  as  it  is  termed,  we  turn  to 
consider  simultaneous  contrast.  What  is  meant  by  this 
will  be  gathered  from  the  following.  Charles  Blanc,  in  his 
“Grammar  of  Painting  and  Engraving,”  tells  us  that  Eugene 
Delacroix,  occupied  one  day  in  painting  yellow  drapery, 
tried  in  vain  to  give  it  the  desired  brilliancy,  and  said  to 
himself,  “How  did  Rubens  and  Veronese  find  such  brilliant 
and  beautiful  yellows  ? ” He  resolved  to  go  to  the  Louvre, 
and  ordered  a carriage.  It  was  in  1830.  At  that  time  in 
Paris  there  were  many  cabs  painted  canary-color.  One  of 
these  was  brought  to  him.  About  to  step  into  it,  he 
stopped  short,  observing  to  his  surprise  that  the  yellow  of 
the  carriage  produced  violet  in  the  shadows.  He  dis- 
missed the  coachman,  entered  his  studio  full  of  emotion, 
and  applied  at  once  the  law  that  he  had  just  discovered, 
which  is,  that  the  shadow  cast  by  an  object  of  a certain 
hue  is  always  slightly  tinged  with  the  complement  of  that 
hue, — a phenomenon  that  becomes  apparent  when  the 
light  of  the  sun  is  not  too  strong,  and  our  eyes,  as  Goethe 
says,  who,  as  Eckermann  tells  us  in  his  “Conversations,” 
made  a similar  discovery,  “ rest  upon  a fitting  background 
to  bring  out  the  complementary.” 

Such  being  the  fact  with  reference  to  simultaneous 
contrast,  to  what  can  we  attribute  it?  Is  it  conceivable 


ATMOSPHERE  AND  LOCAL  COLOR. 


377 


that  it  is  owing  to  any  such  cause  as  that  which  has  just 
been  said  to  be  accepted  as  an  explanation  of  successive 
contrast?  Is  it  probable  that  the  parts  of  the  retina  sur- 
rounding those  on  which  the  colored  image  is  impressed 
could  become  fatigued  because  of  the  latter’s  proximity, 
and  rest  from  fatigue  by  producing  the  complementary 
color?  Hardly.  Yet  it  is  certainly  philosophical  to  at- 
tribute both  simultaneous  and  successive  contrast  to  the 
same  cause — is  it  not?  And  it  is  also  philosophical  to 
attribute  both  of  them  to  a cause  similar  to  that  occasion- 
ing similarly  subjective  effects  in  the  ear.  Moreover,  we 
know  what  causes  these  effects  in  the  ear.  It  is  the  in- 
tensity, rates,  and  shapes  of  certain  sound-waves.  Why  are 
not  the  subjective  effects  in  the  eye  caused  by  the  same 
characteristics  in  sight-waves?  When  the  question  is 
thus  asked,  probably  every  one  who  knows  anything  about 
the  subject  will  be  ready  to  answer,  “ It  would  seem  so.” 
But  if  he  can  give  this  answer,  why  should  he  not  seek  to 
explain  the  phenomena  of  successive  and  simultaneous 
contrasts  by  going  back  to  that  which  is  thus  acknowledged 
to  seem  probable? 

One  reason,  perhaps,  is  that  an  exceedingly  important 
distinction  has  been  overlooked.  It  is  this, — that  the 
organs  or  parts  of  the  organs  that  vibrate  in  the  eye  in 
sympathetic  response  to  the  waves  of  what  we  may  term 
light  in  general , as  in  the  atmosphere,  are  much  more 
susceptible  to  slight  excitation,  i.  e.,  they  are  more  readily 
started  and  kept  in  a vibratory  condition,  than  are  the 
organs  or  parts  of  organs  that  respond  sympathetically  to 
the  waves  of  light  in  particular,  as  in  what  is  termed  local 
color.  This  is  shown  by  the  fact,  among  others,  that  we 
perceive  light  at  dawn,  long  before  we  can  make  out 
either  outlines  or  the  shades  and  tints  that  indicate  them. 


37B  PROPORTION  AND  HARMONY. 

See  also  what  is  said  on  page  381.  Now  in  connection 
with  the  fact  just  mentioned,  which  apparently  must  have 
some  cause  in  the  organism,  let  us  consider  another.  It 
is  the  fact  that  when  color  is  seen  in  an  object,  it  is  be- 
cause the  particles  of  this  object  have  some  effect  corre- 
sponding to  that  produced  by  the  dividing  of  the  rays  of 
light,  through  the  use  of  the  fine  prism  mentioned  on 
page  331.  But  if  such  be  the  case,  two  colors  are  then 
produced,  at  least  potentially.  One  is  seen  by  the  eye. 
What  becomes  of  the  other  color  ? — or  of  the  other  part 
of  the  potentiality  which  was  in  the  light  before  this  other 
color  was  taken  from  it?  Or,  to  state  the  question  in 
terms  of  physics,  if  the  sight-wave  fitted  to  start  in  the  eye 
vibrations 1 giving  a sensation  of  light  in  general , be 
divided,  and  changed  in  form  so  as  to  give  a sensation  of 
color,  must  not  the  rest  of  the  wave  also  be  changed  in 
form  ? It  cannot  be  answered  that  the  whole  of  the  wave 
causing  light  in  general  passes  into  the  form  of  the  particu- 
lar color-wave.  If  it  did,  we  should  have  a condition 
strangely  overlooked  by  physicists  but  that  in  this  case 
would  be  inevitable, — namely,  we  should  not  be  able  to 
distinguish  moonlight  from  a gray  wall  extending  every- 
where in  front  of  us,  or  a pitch-dark  night  from  a black 
wall.  As  things  are,  however,  we  see  at  every  part  of  an 
object,  not  only  light  in  general  but  light  in  particular , — 
i.  e.,  its  own  color.  When  looking  at  the  object,  therefore, 
the  eye’s  organism  must  always  be  influenced  by  two 
forms  of  waves, — those  giving  rise  to  the  sensation  of  light 
in  general , as  in  atmosphere  with  its  various  direct  and 
reflected  rays,  and  those  giving  rise  to  the  sensation  of  the 

1 The  reader  will  observe  that  waves  which  are  external  to  the  eye  are 
one  thing,  and  that  vibrations  within  the  eye  which  are  occasioned  by  the 
waves  are  another  thing. 


ATMOSPHERE  AND  LOCAL  COLOR. 


379 


color  perceived.  But  from  the  forms  of  the  atmospheric 
waves,  in  this  case,  the  wave-forms  of  the  color  have  been 
taken.  What  have  been  left  behind  ? — The  wave-forms 
of  the  complementary  color.  Inasmuch  as  we  see  the 
color  in  the  object  before  us,  the  eye  undoubtedly  is 
under  the  direct  influence  of  these  waves  alone.  They 
exert  a strong  and  positive  effect,  causing  strong  and 
positive  vibrations  in  the  parts  of  the  eye  fitted  to  respond 
to  their  excitation.  But  what  of  the  other  wave-forms  ? 
At  best  their  influence  is  indirect.  They  are  weak  and 
negative,  almost  entirely  suppressed  where  the  color-waves 
are  operating,  and,  at  a slight  distance  from  the  place  where 
they  start,  they  must  pass  like  lesser  waves  at  the  edge 
of  a whirlpool  into  the  forms  of  the  general  light-waves 
of  the  surrounding  atmosphere.  This  would  cause  the 
perception  of  a slight  complementary  color  for  a slight 
distance  on  every  side  of  the  place  in  which  there  was  a 
distinct  perception  of  the  main  color;  and  would  account, 
therefore,  for  simultaneous  contrast.  Now  remove  the 
object  causing  the  color,  what  would  happen?  The  color- 
waves  would  cease  to  excite  vibrations  in  what,  on 
page  377,  were  said  to  be  the  parts  of  the  organs  sus- 
ceptible to  only  comparatively  great  excitation,  and  these 
organs  would  therefore  cease  to  vibrate.  But  how  about 
the  other  organs,  or  parts  of  the  organs, — those  fitted  to 
vibrate  to  the  sensations  of  light  in  general?  Would  they 
cease  to  do  this  ? — Not  as  long  as  there  was  any  light 
visible.  But  what  would  be  the  form  of  their  vibrations 
immediately  after  the  object  occasioning  the  color- waves 
ceased  to  exert  an  influence  ? — What  but  the  form  of  the 
vibrations  caused  by  the  waves  of  light  immediately  sur- 
rounding— and  not  only  so  but  accompanying — the  color- 
waves,  while  these  were  direct,  positive,  and  strong  ? What 


380 


PROPORTION  AND  HARMONY. 


was  this  form  ? It  was  the  form  giving  a sensation  of  light 
in  general  when,  from  that  light,  had  been  taken  the  wave- 
form giving  the  sensation  of  a particular  local  color.  There- 
fore, it  was  the  wave-form  producing  the  complementary 
of  this  local  color.  This  wave-form  of  the  complementary 
had  been  operating  all  the  time.  But  the  strong,  positive 
color-wave  had  kept  it  from  exerting  any  influence  except 
by  way  of  conveying  an  impression  of  light  in  general,  or 
atmosphere,  and,  while  doing  this,  of  producing,  in  places 
near  the  local  color,  the  effects  of  simultaneous  contrast. 
As  soon,  however,  as  the  color-wave  has  ceased  to  exert 
an  influence,  this  wave  of  light  in  general,  which  now  con- 
tains the  potentiality  of  the  complementary  color,  keeps 
the  more  susceptible  vibratory  organism  oscillating  on  till 
after  a little  it  has  assumed  its  usual  condition  representa- 
tive of  all  the  colors. 

As  confirming  this  conception,  let  us  notice  that  the 
suggestions  that  have  been  made  are  not  inconsistent 


See  pages  349,  380,  383. 

with  what  we  know  of  the  formation  of  the  organs  of 
the  eye.  Fig.  130,  represents  the  back  part  of  the 
retina,  and  b the  bacillary  layer  containing  the  rods  and 


PERCEPTION  OF  COLOR  BY  THE  EYE. 


381 


cones,  as  they  are  called.  Where  the  optic  nerve  enters 
the  retina  at  O,  the  eye  is  blind.  This  seems  to  prove 
that  the  bacillary  layer  is  necessary  to  sight.  But  this 
layer  contains  the  rods  and  cones, 
as  represented  in  Fig.  131.  These 
are  said  in  Foster’s  “ Physiology” 
to  be  transparent,  refractive, 
doubly  refractive,  and  very  sensi- 
tive to  light,  changing  in  size  in 
different  degrees  of  it.  Possibly 
they  may  act  in  some  way  analo- 
gously to  prisms.  But  however 
they  may  act,  Fig.  131  shows  that 
the  rods  because  smaller  should 
be  more  sensitive  to  slight  vibra- 
tory effects  than  the  cones ; and 
Fig.  128,  page  350,  shows  that  the 
central  spot,  which  sees  outlines 
and  colors  the  most  distinctly, 
contains  only  cones.  Are  the  rods, 
therefore,  affected,  according  to 
what  was  said  on  page  379,  by  light 
in  general,  and  the  cones  by  local 
color?  Again,  each  rod  and  cone 
possesses  two  entirely  separated 
limbs,  the  larger  of  which  is  nearer 
the  main  body  of  the  nerves  than 
the  smaller.  If  a wave  of  white 
light  affect  each  limb  similarly, 
this  wave  divided  and  changed  in  form,  as  when  color  is 
produced,  must  affect  each  differently.  In  this  case  is  the 
larger  cone-limb  affected  by  the  local  color-wave,  and  the 
smaller,  with  reflecting  rods  near  it,  by  the  twin  com- 


FIG. 


131.— STRUCTURE 
RETINA. 


OF 


r,  cone ; r,  rod  ; z,  inside  ; o , out- 
side. I,  II,  etc.,  different  layers 
as  arranged  from  the  front  where 
light  enters  to  the  back. 

See  pages  349,  381,  383. 


382 


PROPORTION  AND  HARMONY. 


plementary  color-wave?  All  around  the  rods  and  cones, 
and  inside  the  former,  a purplish-blue  liquid  is  constantly 
advancing  and  receding.  It  has  been  supposed  that  the 
sole  purpose  of  this  is  to  record  different  degrees  of  light 
and  shade.  But,  while  recording  these,  it  may  do  very 
much  more.  Most  of  us  must  have  noticed,  when  the 
power  is  turned  from  an  electric  light,  that  the  one  plati- 
num wire  vibrating  at  different  rates  produces  all  the 
warm  colors, — white-yellow,  yellow,  orange,  and  red  ; and 
it  is  a fact  easily  shown  that  these  colors  respectively,  when 
shining  through  blue  glass,  produce  all  the  cold  colors, 
— blue,  green,  olive-green,  and  purple.  The  attributing 
of  articulative  sounds  to  different  rates  and  forms  of 
vibrations  when  affecting  the  same  ossicles  in  the  ear 
suggested  to  Professor  Bell  that  apparatus  for  converting 
the  vibrations  in  an  electric  wire  into  sounds  which  made 
the  telephone  a success.  Why  is  it  not  reasonable  to 
suppose  that  the  same  rods  or  cones,  when  vibrating 
differently,  shaded  or  not  by  blue,  can  produce  all  the 
colors,  so  that  the  mind  can  see  them  as  well  as  the  out- 
lines in  the  picture  impressed  upon  the  retina.  Another 
thought : vibrations  of  particles  of  matter  against  one  an- 
other or  the  air  usually  generate  heat.  Heat  thus  gener- 
ated usually  generates  chemical  action.  Different  rates  of 
vibration — and  this  is  why,  as  has  been  proved,  it  is 
true  of  different  colors — generate  different  degrees  of 
heat  and  of  chemical  action.  Chemical  action,  so  scien- 
tists tell  us,  manifested  in  the  pulling  down  and  build- 
ing up  of  tissue,  is  the  method  through  which  the  nerves 
communicate  sensations.  What  then  ? The  author  is 
aware  that  he  has  suggested  an  explanation  of  the  way  in 
which  sound-waves  or  sight-waves  may  affect  the  organs  of 
the  ear  or  eye,  and  through  them  the  nerves  and  the 


PERCEPTION  OF  COLOR  BY  THE  EYE.  383 

mind  back  of  them,  which  is  not  in  the  books.  But  can 
any  explanation  be  found  in  them  as  plausible,  or  as  free 
from  objections,  as  is  this  one?  Certainly  it  is  not  any 
explanation  ascribing  the  recognition  of  any  pitch  or  color 
to  a separate  organ  fitted  to  respond  sympathetically  to 
it  and  to  it  alone.  So  far,  at  least,  as  concerns  the  organ- 
ism, as  represented  in  Figs.  130  and  13 1,  there  is  no  reason 
to  suppose  otherwise  than  that  all  the  rods  and  cones  may 
be  equally  fitted  to  respond  to  the  waves  of  light  of  any 
color,  and  yet  with  different  degrees  of  susceptibility,  some 
— possibly  the  rods — representing  only  atmospheric  light 
and  color,  and  some — possibly  the  cones — that  color  which 
appears  to  be  local. 

The  explanation  thus  suggested  not  only  refers  to  a 
similar  cause  the  subjective  effects  both  in  the  ear  and 
the  eye,  and,  in  the  latter,  both  successive  and  simul- 
taneous contrast,  but  it  seems  to  explain  also  the  most 
important  difference  between  the  effects  of  successive  and 
of  simultaneous  contrast.  This  is  that  the  time  of  the 
continuance  and  the  brilliancy  of  a color  in  successive  con- 
trast depend  upon  the  length  and  strength  of  the  vibra- 
tory condition  preceding  it,  whereas,  in  simultaneous 
contrast,  such  effects  depend  neither  upon  the  length  of 
time  during  which  one  looks  at  a color,  nor  even  upon  its 
comparative  fulness.  This  difference  is  exactly  what,  ac- 
cording to  our  hypothesis,  we  should  expect.  According 
to  it,  the  continuance  and  character  of  the  oscillations  oc- 
casioning successive  contrast  will,  of  course,  be  deter- 
mined by  the  quantity  and  quality  of  their  previous 
excitation.  On  the  contrary,  the  complementary  color 
produced  in  simultaneous  contrast  depends  upon  the 
presence  by  its  side  of  the  local  color,  and  it  is  neither 
increased  nor  lessened  in  intensity  by  its  continued  pres- 


3^4 


PROPORTION  AND  HARMONY. 


ence.  Moreover,  in  every  place  where  this  complementary 
hue  can  become  visible,  there  is  already  some  other  shade 
or  tint  with  which  its  hue  must  blend,  and  doing  so,  ac- 
cording to  the  laws  of  color,  it  must  always  produce  a 
mixed,  and  therefore  never,  save  in  very  exceptional  cases, 
a brilliant  effect. 

Even  if  the  explanations  of  these  phenomena  thus  sug- 
gested may  do  nothing  toward  rendering  them  and  their 
bearings  upon  the  subject  before  us  more  intelligible,  they 
may,  at  least,  serve  to  emphasize  certain  facts  which, 
as  facts,  are  indisputable.  The  most  important  of  these  is 
that  all  colors  have  the  effect  of  imparting  the  tints  of 
their  complementaries  to  any  surface  adjoining  their  own. 
In  such  cases,  if  the  surface  have  no  color,  they  give  it 
colors ; if  it  have  their  complementary  color,  they  make 
this  more  brilliant  ; if  it  have  some  other  color  yet  not 
their  own,  they  cause  this  and  their  complementary  to 
blend  and  produce  a mixed  color  different  from  either. 

In  the  production  of  these  complementary  tints  most 
important  influences  are  traceable  to  degrees  of  light  and 
shade.  Experiments  with  the  color-top  show  that  when 
disks  are  so  arranged  that  a single  color  is  both  on 
the  circumference  and  in  the  centre,  while  a narrow  circu- 
lar band  of  white  and  black  is  between  them, — that  in 
this  case,  during  the  revolution  of  the  top,  this  circular 
band  appears  to  be  not  gray  {i.  e.,  white  and  black)  but  of 
a color  complementary  to  that  on  either  side  of  it.  This 
is  as  we  should  expect.  But  it  has  been  found  also 
that,  in  such  an  arrangement,  the  warm  colors  produce 
the  brightest  complementaries  when  there  is  more  black 
than  white  in  this  circular  band,  and  that  the  cold  colors 
do  the  same  when  there  is  more  white  than  black  in  it. 
The  reason  is  evident.  The  warm  colors  are  brighter 


COLORS  WHEN  SIDE  BY  SIDE . 


385 


than  their  complementaries  and  the  cold  colors  darker. 
By  consequence,  the  most  favorable  conditions  for  pro- 
ducing a complementary  are  present  when  the  warm 
colors  are  brighter  and  the  cold  darker  than  the  gray 
which  is  beside  them.  As  each  different  color,  too,  repre- 
sents a different  degree  of  dark  or  light  of  course  the 
gray,  which  is  to  receive  the  contrast,  must  represent  a cor- 
responding degree  of  light  or  dark.  It  is  important  to  no- 
tice, besides  this,  that  the  cold  colors,  because  they  have 
warm  or  bright  complementaries,  invariably  produce 
stronger  contrasts  on  neutral  hues  than  do  the  warm 
colors,  for  which  reason  it  is  often  less  difficult  to  obtain 
quiet,  unobtrusive  effects  through  using  the  warm.  Now 
let  us  consider  the  influence  of  these  near  colors  on  a 
neutral  ground  as  produced  by  different  shades  and  tints. 
If,  in  trying  the  experiment  with  the  color-top  just  men- 
tioned, we  take  full  colors  and  look  at  them  in  bright  sun- 
light, we  hardly  perceive  any  complementary  color  at  all 
cast  on  the  gray.  In  the  darkened  corner  of  a room, 
however,  where  the  colors  appear  no  longer  full  but  dark, 
the  contrasting  color  is  often  very  vivid.  Again,  if  instead 
of  full  colors  we  take  broken  colors,  i.  e.,  colors  mixed 
with  much  white,  the  complementaries  appear  vivid  even 
in  sunlight.  Accordingly,  we  see  that  the  conditions 
most  favorable  for  producing  contrasts  on  a neutral 
ground  are  realized  when  we  use  dark  colors,  or  broken. 
The  explanation,  more  psychological  than  physical,  which 
is  ordinarily  given  for  these  facts,  as  stated  by  Von  Bezold, 
is  that  “ the  eye  is  most  sensitive  to  the  contrasting  colors 
in  those  cases  in  which,  on  account  of  the  darkness  or 
paleness  of  the  colors,  it  is  left  in  uncertainty  as  to  the  hue 
of  the  ground,  that  is  to  say,  the  hue  of  the  inducing  color 

actually  present.”  A better  explanation  seems  obtain- 
25 


386 


PROPORTION  AND  HARMONY. 


able  by  recalling  the  fact  that  a complementary  is  always 
produced  by  the  rays  representing  the  difference  between 
a full  color  and  white  light.  A color  is  dark  because 
it  contains  comparatively  little  light,  and  pale  or  broken 
because,  in  connection  with  much  light,  it  contains  com- 
paratively little  color.  In  these  circumstances  the  com- 
plementary, because  it  contains  either  more  light  or  more 
color  than  the  hue  producing  it,  appears  brighter  than  it 
would  otherwise, — a statement  which  accords  with  the 
facts  already  noticed  (see  page  334),  that  dark  colors  have 
light  complementaries,  which  they  produce  best  on  light- 
colored  surfaces ; while  light  colors  have  dark  comple- 
mentaries, which  they  produce  best  on  dark  surfaces.  In 
connection  with  this,  it  is  well  to  notice  that  a black  sur- 
face receives  a complementary  color  only  in  the  degree  in 
which  it  contains  some  gloss  or  light,  which  is  an  additional 
reason  for  supposing  that  the  presence  or  absence  of  light 
is  that  which  determines  the  strength  of  the  contrast. 

Now  let  us  examine  the  effects  of  complementary  colors 
not  on  neutral  but  on  colored  surfaces.  Here  we  notice 
that  when  two  of  these  surfaces  are  placed  in  juxtaposi- 
tion, each  appears  as  if  some  of  the  complementary  of  the 
other  had  been  mixed  with  it.  Of  course,  the  laws  ap- 
plying to  the  blending  of  colors  with  neutral  gray  apply 
here  ; and  to  refer  once  more  to  the  subject  that  we  have 
just  left,  a confirmation  of  the  view  presented  in  the  last 
paragraph  may  be  found  in  the  fact  that  invariably  very 
light  broken  colors  are  those  that  impart  their  comple- 
mentaries most  strongly.'  For  this  reason,  such  colors 
are  peculiarly  adapted  for  brilliant  effects  ; and  we  find 
them  used  for  this  purpose  almost  exclusively  by  the 
great  colorists  of  Venice  and  the  Netherlands. 

1 The  following,  from  Professor  Rood’s  “ Modern  Chromatics,”  chapter 


COLORS  WHEN  SIDE  BY  SIDE. 


3 87 


Before  leaving  this  subject  it  may  be  of  interest  to 
notice  three  prominent  ways  of  using  contrasts  in  order 
to  relieve  objects  from  their  backgrounds.  They  are 
taken  from  Von  Bezold’s  “Theory  of  Color.” 

I.  The  object  may  be  a silhouette,  light  against  a dark 
ground,  or  dark  against  a bright  ground.  In  both  cases 
usually,  and  in  the  latter  case  almost  necessarily,  the 
warm  color  should  be  in  the  foreground. 

II.  The  light  parts  of  the  object  may  be  lighter  than 
the  ground  and  the  dark  parts  darker.  Applied  to  color- 
ing, this  is  best  exemplified  where  neutral  tints  are  given 
to  the  ground,  while  near  objects  are  made  warmer  than 
the  ground  in  their  warm  parts,  and  colder  in  their  cold 
parts. 

III.  The  bright  side  of  the  object  may  be  placed  on  a 

xv.,  p.  245,  indicates  the  changes  produced  upon  each  other  by  the  more 
important  colors  when  thus  brought  together. 


CHANGES  DUE  TO  CONTRAST  IN  PAIRS  OF  COLORS. 


Red becomes  more  purplish. 

and 

Orange “ 44  yellowish. 

Red 44  “ purplish. 

and 

Yellow 44  44  greenish. 

Red 44  44  brilliant. 

and 

Blue-green 44  44  brilliant. 

Red 44  4 4 orange-red. 

and 

Blue 44  44  greenish. 

Red 44  4 4 orange-red. 

and 

Violet 44  44  bluish. 

Orange 44  44  red-orange. 

and 

Yellow 44  44  greenish- 

yellow. 

Orange 44  44  red-orange. 

and 

Green 44  44  bluish- 

green. 

Orange 44  44  brilliant. 

and 

Cyan-blue 44  44  brilliant. 


Orange 

becomes 

more  yellowish. 

and 

Violet 

it 

44  bluish. 

Yellow 

u 

44  orange- 

and 

yellow. 

Green 

44  bluish- 

green. 

Yellow 

4 4 orange- 

and 

yellow. 

Cyan-blue 

44  blue. 

Yellow 

K 

44  brilliant. 

and 

Ultramarine-blue. 

u 

44  brilliant. 

Green 

il 

44  yellowish- 

and 

green. 

Blue 

44  purplish. 

Green  

tl 

44  yellowish- 

and 

green. 

Violet 

44  purplish. 

Greenish-yellow  . 

It 

44  brilliant. 

and 

Violet 

44  brilliant. 

Blue 

It 

44  greenish. 

and 

Violet 

44  purplish. 

388 


PROPORTION  AND  HARMONY. 


dark  ground,  and  its  shaded  side  on  a light  ground  ; i.  e., 
the  warm  side  of  an  object  may  be  placed  against  a cold 
ground,  and  the  cold  side  against  a warm  ground.  This 
was  the  usual  method  of  the  painters  of  the  Netherlands, 
and  is  adopted  very  generally  by  the  best  painters  of 
our  own  times. 


CHAPTER  XXIII. 


COLOR-SCALES. 

Object  of  this  Chapter — Colors  can  be  Used  together  that  Differ  either  Slightly 
or  Greatly — Theory  that  Two,  Three,  or  More  can  be  Used  together  if 
they  Make  White — Theory  Based  on  Construction  of  Color-Scales  : 
Von  Bezold’s  of  Twelve  Colors — Rood’s  Summary  of  Combinations  of 
Colors  Founded  on  Experience — Combinations  Determined  as  in  Musi- 
cal Harmony  by  Ratios  between  the  Numbers  of  Vibrations  a Second 
Causing  the  Colors — All  the  Colors  can  Represent  only  the  Ratios 
Possible  to  a Single  Scale — Compensating  Possibility  of  Variety  in 
Each  Color — Correspondences  Need  to  be  Found  only  between  the 
Ratios  Underlying  the  Harmonic  Notes  and  the  Harmonic  Colors — 
The  Ratio  Expressive  of  the  Two  Chief  Harmonics  of  Music  aside 
from  that  of  the  Octave,  which  has  no  Analogue  in  Color — The  Same 
Ratio  as  Applied  to  Color — The  Tonic  and  Dominant  Harmonize  all 
the  Notes  of  the  Scale  as  the  Two  Complementaries  Contain  all  the 
Colors  of  the  Spectrum — The  Tonic  and  Dominant  Represent  the 
Same  Ratios  as  the  Complementaries — Reasons  for  Apparent  Excep- 
tions— Ratios  Expressive  of  the  Three  Harmonics  in  the  Major  Triad  of 
Music — Same  Ratios  Applied  to  Triads  of  Colors — Recapitulation — A 
Fourth  Color  would  Naturally  Correspond  to  the  Seventh  in  Music,  a 
Result  Approximating  that  Reached  by  Von  Bezold — The  Reason  why 
Notes  and  Colors  thus  Related  Satisfy  the  Senses — Similarity  of 
Method  in  Determining  Consonance  either  in  Sound  or  Color, 

w HAT  has  been  said  of  the  complementary  colors 
will  aid  us  in  deciding  what  other  colors  are  fitted 
to  go  together.  For  reasons  already  given,  the  principles 
underlying  this  subject  apply  more  absolutely  to  decora- 
tion than  to  pictures,  but,  just  as  arrangements  of  sound 
in  verse  are  satisfactory  in  the  degree  in  which  they  ful- 
fil such  laws  of  harmony  as  apply  to  music,  so  arrange- 

389 


390 


PROPORTION  AND  HARMONY. 


merits  of  colors  in  pictures  are  satisfactory  in  the  degree 
in  which  they  fulfil  such  laws  of  harmony  as  apply  to 
decoration.  Although  the  painter  of  pictures  does  not  use 
color  merely  for  its  own  sake,  he  ought  nevertheless  to 
use  it  in  such  a way  as  to  cause  it,  for  its  own  sake,  to  be 
a source  of  interest  and  pleasure. 

Glancing  back  at  the  scale  of  colors  indicated  in  Von 
Bezold’s  chart,  Fig.  127,  page  334,  the  first  thought 
that  suggests  itself  is  that  slight  differences  in  color  can 
go  together  in  case  they  be  no  greater  than  we  are  accus- 
tomed to  see  produced  by  different  degrees  of  light  upon 
different  parts  of  the  same  fabric,  and  which  result  in  no 
more  than  different  tints  or  shades  of  the  same  hue.  In 
this  case,  as  stated  on  page  347,  though  the  color-waves 
differ  in  intensity  and  extent,  they  do  not  necessarily 
differ  in  rate  or  shape.  This  is  not  true,  however, 
when  we  come  to  colors  between  which  there  are  not 
slight  but  decided  differences,  colors  separated  by  what 
Von  Bezold  in  his  chart  (page  334)  would  term  a whole 
interval.  Suppose  that  two  of  these  be  in  juxtaposition. 
Each,  as  we  know,  casts  its  complementary  on  the  other. 
But  this  complementary  is  on  the  opposite  side  of  the 
chart,  separated  as  far  as  any  color  can  be  from  that 
on  which  it  is  cast.  The  result  is  that  when  the  two,  the 
complementary  and  the  color  that  receives  it,  are  mixed, 
the  change  is  as  great  as  can  possibly  be  produced  by  a 
mixture  of  this  kind.  For  instance,  if  red  and  violet  be 
side  by  side,  bluish-green  mixes  with  the  violet,  tending 
to  give  it  a bluish  cast,  and  green  mixes  with  the  red, 
tending  to  give  it  a yellowish  cast.  The  two  colors,  there- 
fore, when  placed  together,  appear  to  differ  more  than  they 
really  do.  This  suggests  a law  applicable  universally  to 
the  arrangement  of  colors,  viz.,  that  when  in  juxtaposi- 


COLOR-SCALES. 


391 


tion,  those  which  differ  the  least,  change  each  other’s 
peculiar  hues  the  most ; and  sometimes  dim  them  greatly. 
The  reverse  is  also  true,  namely,  that  colors  which  differ 
the  most,  change  each  other’s  peculiar  hues  the  least. 
On  the  contrary,  they  often  reinforce  them  and  render 
them  more  brilliant.  This  is  so  because  the  colors  that 
differ  the  most,  in  the  sense  of  being  the  farthest  apart  on 
the  chart  of  colors,  are  those  that  are  complementary,  like 
red  and  bluish-green,  for  instance. 

Having  found  out  which  colors,  when  adjoining,  have 
the  worst  effects  upon  one  another,  and  which  the  best 
effects,  we  are  prepared  to  understand  other  principles 
that  have  come  to  be  accepted  with  reference  to  the 
general  subject.  For  arriving  at  these  principles,  sev- 
eral different  methods  are  worthy  of  consideration,  the 
results  of  which,  however,  are  not  essentially  different, 
and  all  of  which  appear  to  contain  elements  of  truth.  To 
begin  where  we  left  off,  it  seems  to  be  a logical  deduction, 
from  what  has  been  said,  that  any  colors  can  be  placed 
together  which  together  make  white.  These  may  be  in- 
cluded in  three  classes:  I.  Any  two  which  together  make 
white,  i.  e. , the  complementary  colors;  as  red  and  bluish- 
green,  orange  and  turquoise-blue,  yellow  and  ultramarine, 
yellowish-green  and  violet,  and  green  and  purple.  II. 
Any  two  which,  mixed  with  one  another’s  complement- 
aries,  can  make  white  ; as  red  and  turquoise-blue,  for 
instance,  because  the  red  imparts  a bluish-green  tint  to 
the  turquoise-blue,  and  the  turquoise-blue  an  orange  tint 
to  the  red.  Undoubtedly,  some  of  the  most  effective 
combinations  or  pairs  of  colors,  not  complementary,  may 
be  accounted  for  according  to  this  rule.  The  two  are 
harmonious  because,  especially  when  one  of  the  colors  is 
very  bright,  like  vermilion,  orange,  or  yellow,  it  is  possi- 


392 


PROPORTION  AND  HARMONY. 


ble  for  the  two,  when  in  combination,  to  fulfil  the  principle 
causing  us  to  use  complementaries  even  better  than  would 
complementaries  themselves.  It  is  this  fact,  probably, 
that  accounts  for  the  satisfaction  taken  in  the  combina- 
tions of  the  colors  brought  together  by  the  application  of 
the  first  rule  of  Von  Bezold,  given  below,  the  colors  to 
which  it  applies  being  the  same  as  those  to  which  the  rule 
now  being  considered  applies,  and  very  nearly  the  same  as 
the  colors  formerly  supposed  to  be  complementary.  But 
before  we  pass  to  Von  Bezold’s  rules,  we  must  add  the 
following  to  the  two  principles  already  mentioned:  III. 
Any  three  (and  sometimes  any  number  of)  colors  can  go 
together  which  together  or  mixed  with  one  another’s  com- 
plementaries can  make  white.  This  rule  applies  to  the  old- 
fashioned  primaries,  red,  yellow,  and  blue,  and  to  the 
secondaries,  orange,  green,  and  purple  ; in  short,  it  reaches 
a result  practically  the  same  as  that  following  the  appli- 
cation of  Von  Bezold’s  second  rule,  which  will  be  given 
in  a moment. 

Von  Bezold,  in  determining  what  colors  should  be  placed 
together,  drops  altogether  the  Field  theory  that  those 
should  be  used  which  together  make  white.  In  lieu  of 
this,  he  divides  all  the  colors  into  twelve  and  arranges 
them  on  a scale  (see  Fig.  127,  page  334)  intended  to  rep- 
resent much  what  the  scale  of  twelve  half-tones  represents 
in  music.  This  scale  is  drawn  up,  as  he  says  (chapter  iii., 
page  1 14),  on  the  principle  of  having  it  show“  how  the  color- 
chart  would  look  if  the  lines  of  division  were  so  arranged 
that  the  apparent  difference  in  the  hue  of  the  color 
between  each  two  compartments  would  remain  the  same 
upon  the  whole  of  the  circumference.”  His  first  rule,  a 
suggestion  with  reference  to  which  has  been  made  above, 
is  that  any  two  colors  can  be  placed  together  which 


COLOR-SCALES. 


393 


are  separated  in  this  scale  by  six  intervals,  i.  e.,  beginning 
with  purple, 


Experience  has  shown,  he  says,  that  these  form  even 
better  combinations  than  do  the  complementary  colors. 
His  second  rule,  to  which  reference  is  also  made  on  page 
392,  is  that  any  three  colors  can  go  together  which  are 
separated  by  four  intervals,  i.  e., 


His  third  rule,  applying  to  four  colors,  is  not  what  might 
be  expected,  viz.,  to  take  those  separated  on  the  chart  by 
three  intervals.  This,  he  says,  would  bring  into  proximity 
colors  too  nearly  connected  on  the  chart ; and  it  would 
also  produce  the  effect  of  two  pairs  without  indicating  a 
design  to  do  so.  Instead  of  this,  he  advises  marking  the 
effect  strongly  by  taking  two  pairs, — as,  for  example, 
purple  and  green,  carmine  and  turquoise-blue, — one  in 
each  of  which  is  near  one  in  the  other,  and  then  arranging 
all  the  colors  so  that  the  near  colors  shall  not  meet. 

In  this  connection,  the  reader  will  be  pleased  to  have 
brought  to  his  attention  the  exceedingly  interesting  and 
suggestive  summary  with  reference  to  certain  combinations 
of  colors  given  in  chapter  xvii.  of  Rood’s  “ Modern 
Chromatics.”  The  reasons  for  the  agreeableness  or  the 
opposite  of  many  of  these  combinations,  he  says,  “ can- 
not be  solved  by  the  methods  of  the  laboratory,  or  by 
the  aid  of  a strictly  logical  process,”  but,  nevertheless,  what 


Purple  and  Green. 

Carmine  and  Bluish-green. 
Vermilion  and  Turquoise-blue. 


Orange  and  Ultramarine. 

Yellow  and  Bluish-violet. 
Yellowish-green  and  Purplish-violet. 


Purple,  Yellow,  and  Turquoise-blue. 
Carmine,  Yellowish-green,  and  Ultramarine. 
Vermilion,  Green,  and  Bluish-violet. 

Orange,  Bluish-green,  and  Purplish-violet. 


394 


PROPORTION  AND  HARMONY. 


is  said  of  them  seems  to  accord  in  the  main  with  practical 
experience.  The  tables  are  in  the  note  below.1 

The  third  method  of  arriving  at  the  principles  underly- 
ing the  joining  of  colors  is  advocated  by  those  who  hold 
that  as  in  music  the  ratios  between  the  numbers  of  vibra- 

1 Spectral  Red  (a  red  between  carmine  and  vermilion)  with  blue  gives  its 
best  combination — with  green  gives  a strong  but  rather  hard  combination — 
with  yellow  gives  an  inferior  combination — with  red  lead  gives  a bad  com- 
bination— with  violet  gives  a bad  combination.  If  gold  be  substituted  for 
the  yellow  pigment,  the  combination  becomes  excellent.  Red  and  yellow 
also  make  a better  combination  when  the  red  inclines  to  purple  and  the 
yellow  to  greenish-yellow.  The  combination  red  And  yellow  is  also  improved 
by  darkening  the  yellow  or  both  colors  ; this  causes  the  yellow  to  appear  like 
a soft  olive-green.  The  combination  red  and  green  is  also  improved  by 
darkening  both  colors,  or  the  green  alone. 

Vermilion  with  blue  gives  an  excellent  combination — also  with  cyan- 
blue — with  green  gives  an  inferior  combination — also  with  yellow — with 
violet  it  gives  a bad  combination.  Vermilion  and  gold  furnish  an  excellent 
combination.  The  combination  vermilion  and  yellow  is  improved  somewhat 
by  darkening  the  yellow  ; if  it  is  considerably  darkened,  it  tells  as  a soft 
olive-green.  Vermilion  and  green  are  better  when  the  green  or  both  colors 
are  much  darkened. 

Red  Lead  with  blue  gives  an  excellent  combination — also  with  cyan-blue 
— with  blue-green  gives  a strong  but  disagreeable  combination — rndb.  yellow- 
ish-green gives  a tolerably  good  combination — with  yellow  gives  quite  a good 
combination — also  with  orange.  The  combination  red  lead  and  bluish-green 
is  improved  by  darkening  the  green  or  both  the  colors  (R.).  Red  lead  gives 
a better  combination  with  a yellow  having  a corresponding  intensity  or  sat- 
uration ; if  the  yellow  is  too  bright  the  effect  is  inferior.  The  combination 
red  lead  And  yellow  is  much  better  than  red  and  orange. 

Orange  with  cyan-blue  gives  a good  and  strong  combination — also  with 
ultramarine — with  green  gives  a good  combination — with  violet  gives  a 
moderately  good  combination. 

Orange-Yellow  with  ultramarine  gives  its  best  combination — with  cyan- 
blue  gives  not  quite  so  good  a combination — with  violet  gives  a good  combi- 
nation— also  with  purple — with  purple-red  gives  an  inferior  combination 
— with  spectral  red  gives  an  inferior  combination — with  sea-green  gives  a 
bad  combination. 

Yellow  with  violet  gives  its  best  combinations — with  purple-red  gives  good 


COLOR-SCALES. 


395 


tions  per  second  producing  the  different  notes  determine 
which  should  go  together,  so,  in  painting,  the  ratios  be- 
tween the  numbers  of  vibrations  per  second  producing 
the  different  colors  should  determine  this.  As  a rule, 

combinations — also  with  purple — with  spectral  red  gives  inferior  combina- 
tions— with  blue , inferior  to  orange-yellow  and  blue— with  blue-green  gives 
one  of  the  worst  possible  combinations — with  green  gives  bad  combinations. 
The  combination  yellow  and  spectral  red  is  improved  by  darkening  the 
yellow.  Blue-green  and  yellow,  both  much  darkened,  give  a better  combi- 
nation. According  to  Chevreul,  yellow  gives  with  green  a good  and  lively 
combination  ; to  this  the  author  cannot  agree,  although  it  is  true  that  the 
effect  is  improved  by  darkening  the  yellow  considerably.  Chrome-yellow 
and  emerald-green  give  combinations  that  are  not  bad  when  both  the  colors 
are  very  much  darkened. 

Greenish-Yellow  with  violet  gives  its  best  combinations — with  purple 
gives  good  combinations — also  with  purplish-red — with  vermilion  gives 
strong  but  hard  combinations — with  spectral  red  gives  strong  but  hard  com- 
binations— with  red  lead  gives  tolerably  good  combinations — with  orange- 
yellow  gives  bad  combinations — also  with  cyan-blue — with  ultramarine  gives 
a somewhat  better  combination.  The  combination  greenish-yellow  and 
orange-yellow  is  improved  by  darkening  the  latter  color,  which  then  appears 
brownish.  Greenish-yellow  and  cyan-blue  make  a better  combination  when 
the  blue  is  darkened. 

Grass-Gref.n  with  violet  gives  good  but  difficult  combinations — also  with 
peirple-violel — with  rose  gives  combinations  of  doubtful  value — also  with 
carmine — also  with  pink — also  with  blue.  The  value  of  the  last  four  com- 
binations is  a disputed  matter.  The  combination  green  and  carmine  is  im- 
proved by  darkening  both  colors  considerably  (R.).  The  combination 
green  and  blue  becomes  better  as  the  green  inclines  to  yellow  and  the  blue  to 
violet.  The  combination  green  and  violet , according  to  Chevreul,  is  better 
when  the  paler  hues  of  these  colors  are  employed. 

Emerald-Green  with  violet  gives  strong  but  hard  combinations — also 
with  purple — also  with  red — also  with  orange — with  yellow  gives  bad  combi- 
nations. All  these  combinations  are  very  difficult  to  handle.  Emerald- 
green  and  yellow,  when  both  are  much  darkened,  furnish  somewhat  better 
combinations. 

Sea-Green  with  vermilioti  gives  good  combinations — also  with  red  lead 
— also  with  violet — with  purple-violet  gives  tolerably  good  combinations — 
with  purple-red  gives,  simply  as  pairs,  poor  combinations — with  carmine 
gives,  simply  as  pairs,  poor  combinations — with  blue  gives  bad  combinations 


396 


PROPORTION  AND  HARMONY. 


physicists  have  had  little  respect  for  any  advocate  of  this 
theory,  because  he  has  usually  started  out  with  the 
hypothesis  that  there  is  some  absolute  and  necessary  con- 
nection between  the  seven  colors  of  the  spectrum  and  the 

— also  with  yelloiu.  The  surface  of  the  green  should  be  much  larger  than 
that  of  the  vermilion  or  red  lead. 

Cyan-Blue  with  chrome-yellow  gives  moderate  combinations — with  Naples 
yellow  gives  good  combinations — also  with  slraw-yellow — also  with  carmine 
(light  tones) — with  violet  gives  poor  combinations — also  with  purple-violet — 
with  ultramarine  gives  good  combinations  (small  interval).  The  combi- 
nations of  cyan-blue  with  violet  and  purple-violet  are  not  good  except  in  fine 
materials  and  light  tones. 

Ultramarine  with  carmine  gives  poorer  combinations  than  cyan-blue — 
with  purple-red  gives  poorer  combinations  than  cyan-blue — with  purple  gives, 
simply  as  pairs,  poor  combinations. 

Violet  with  purple  gives  poor  combinations  if  extended  beyond  the  small 
interval — with  carmine  gives  poor  combinations. 

The  triads  that  have  been  most  extensively  used  are  : I.  Spectral  red , 

yellotv , blue.  II.  Purple-red , yellow , cyan-blue.  III.  Orange , green , 

violet.  IV.  Orange , green , purple-violet.  V.  Carmine , yellow , and  green 
was,  according  to  Briicke,  a triad  very  much  used  during  the  Middle  Ages, 
though  to  us  the  combination  is  apt  to  appear  somewhat  hard  and  unrefined. 
Here  we  have  two  warm  colors  (see  page  327),  but  contrast  is  twice  sacrificed  ; 
that  is,  slightly  in  the  case  of  the  carmine  and  yellow,  and  more  with  the 
yellow  and  green.  VI.  Orange-yellow , violet , and  bluish-green  is  an  exam- 
ple of  a combination  which  is  poor  not  from  defect  of  contrast,  but  because 
it  contains  two  cold  colors,  one  of  them  being  the  coldest  in  the  chromatic 
circle.  VII.  Vermilion , green , and  violet-blue  is  a triad  which  has  been 
extensively  used  in  some  of  the  Italian  schools.  At  first  sight  we  have  here 
apparently  two  cold  colors  ; but  as  the  green  was  olive-green,  the  combi- 
nation really  amounts  to — VIII.  Vermilion , dark  greenish-yellow,  and  violet- 
blue,  and  corresponds  in  principle  with  those  given  above. 

In  the  employment  of  any  of  these  triads  in  painting  or  in  ornament,  the 
artist  can  of  course  vary  the  hue  of  the  three  colors  through  the  small  interval 
without  destroying  the  definite  character  of  the  chromatic  composition  ; and 
even  small  quantities  of  foreign  colors  can  also  be  added.  When,  however, 
they  begin  to  assume  importance  in  the  combination,  they  destroy  its  peculiar 
character.  White  or  gray  can  be  introduced,  and  one  of  these  is  often  used 
with  a happy  effect,  particularly  in  the  triads  orange,  green,  violet ; purple- 
red,  yellow,  cyan-blue. — Abbreviated  from  Rood’s  “ Modern  Chromatics.” 


COLOR-SCALES. 


39  7 


seven  notes  of  the  musical  scale.  As  was  shown,  however, 
in  Chapter  XIV.  of  “ Rhythm  and  Harmony  in  Poetry 
and  Music,”  these  seven  notes  happen  to  be  used  merely 
as  a matter  of  convenience.  There  have  been  scales  ex- 
tensively used  of  four  and  six  notes,  and  possibly  our 
own  might  be  improved  by  the  addition  of  two  more. 
As  it  is,  it  contains  not  seven  but  twelve  distinct  inter- 
vals. There  is  a principle,  however,  underlying  the 
formation  of  all  musical  scales,  as  well  as  of  all  melody 
and  harmony,  which  depends  upon  the  relative  numbers 
of  vibrations.  One  cannot  refrain  from  feeling,  therefore, 
that  it  is  logical  to  suppose  that  this  same  principle  should 
be  exemplified  in  that  which  causes  colors  to  harmonize. 

It  does  not  allay  this  feeling,  to  remind  one  that  between, 
say,  the  400  trillions  of  vibrations  causing  extreme  red 
and  the  750  causing  extreme  violet,  the  sum  total  of  vibra- 
tions does  not  correspond  to  those  of  a single  octave.  It 
does  correspond  to  the  musical  scale,  so  far  as  this  can  be 
produced  without  doubling  one  of  its  notes.  It  corre- 
sponds to  all  the  intervals  between  do  and  si  inclusive.  If 
an  upper  do  were  represented,  then,  to  make  everything 
consistent,  an  upper  re , mi,  etc.,  should  be  represented. 
Otherwise  one  of  the  colors — that  corresponding  to  do — - 
would  have  double  the  value  of  each  of  the  others.  As 
it  is,  we  have  in  the  colors  all  the  range  of  intervals  corre- 
sponding to  those  of  a single  octave  without  encroaching 
upon  a second.  The  possibility,  however,  of  producing 
variations  in  a single  color  is  much  greater  than  that  of 
doing  the  same  in  a single  sound.  Indeed,  when  we  con- 
sider the  innumerable  shades  and  tints  not  merely  of  one 
color  but  of  all  other  colors  in  connection  with  which 
this  one  may  produce  mixed  effects,  we  are  forced  to 
recognize  that  the  range  both  of  single  colors  and  of 


39§ 


PROPORTION  AND  HARMONY. 


those  that  are  exactly  complementary  to  these  is  practi- 
cally infinite,  and  thus  far  more  than  sufficient  to  make 
up  for  the  absence  in  the  color-scale  of  more  than  one 
octave. 

So  much  for  the  theory;  now  for  the  facts  confirming 
it.  Let  us  take  the  ratios  of  the  numbers  of  vibrations 
producing  the  sounds,  not  of  all  the  scale,  but  of  those 
that  harmonize,  and  apply  these  ratios  to  the  numbers  of 
vibrations  producing  the  different  colors,  and  notice  what 
colors  they  cause  to  go  together.  As  the  numbers  of 
vibrations  producing  the  colors  are  exceedingly  great,  and 
the  difficulty  in  the  spectrum  of  determining  just  where 
one  color  leaves  off  and  another  begins  is  also  great,  we 
must  content  ourselves  with  approximate  measurements, 
but  even  with  these  we  can  attain  our  object.  Let  Von 
Bezold,  too,  who  is  opposed  to  this  theory,  confirm  it  by 
the  numbers  representing  tens  of  trillions  of  vibrations 
which  he  has  indicated  for  the  colors  placed  in  his  chart 
(Fig.  127,  page  334),  and  by  the  lines  indicating  single 
degrees  of  these  with  which  he  has  divided  the  next  to 
the  outer  circle. 

In  any  given  musical  scale — aside  from  the  notes  that 
are  an  octave  apart,  represented  by  the  ratio  1 : 2,  and 
with  which  there  is  nothing  in  color,  as  has  been  said,  to 
correspond — the  notes  most  nearly  related — to  take  them 
as  represented  in  the  scale  of  C — are  C,  c,  and  g.  This 
may  be  recognized  by  a single  glance  at  the  partial 
tones,  as  indicated  in  the  music  on  page  341.  In  that, 
the  numbers  1,  2,  3,  4,  etc.,  will  be  observed  just  at  the 
left  of  the  notes  respectively  marked  by  the  letters  C',  C, 
g,  and  c.  The  numbers  represent,  in  another  way,  the 
same  as  those  used  by  Pythagoras,  when  he  divided  a 
string  into  two,  three,  four,  etc.,  parts,  and  found  the  note 


COLOR-SCALES. 


399 


produced  by  each  part  to  be  in  harmony  with  that  pro- 
duced by  the  whole  string  and  by  each  other  part.  The 
numbers  represent  also  that  C' : C ::  I : 2,  that  C : g ::  1:3, 
and  C'  : c ::  1 : 4,  as  well  as  that  C : g ::  2 : 3 and  g : c ::  3 : 4. 
Our  object  now  is  to  find  the  relationships  of  two  notes 
contained  within  the  limits  of  the  same  octave  that  can 
represent  the  relationships  between  the  particular  C or  c 
and  the  g that  we  wish  to  use.  Shall  we  take  C : g ::  2 : 3, 
or  g:  023:4?  In  which  of  the  two  formulae  are  both 
factors  most  nearly  related  in  the  same  way  to  the  funda- 
mental base  C'  ? Is  it  not  in  g : c ::  3 : 4 ? In  this,  g is  the 
third  note  from  C' ; and  c,  though  the  fourth  note,  is  the 
third  c from  C'  ; and  g is  related  to  the  whole  lower  octave 
C'-C  precisely  as  c is.  Is  not  this  ratio  of  3:4,  there- 
fore, the  one  best  fitted  to  represent  the  ratio  between  the 
complementary  colors?  Here,  as  in  other  places,  a refer- 
ence to  music  may  assist  us.  The  most  important  chords 
in  harmonizing  the  notes  of  any  scale  are  undoubtedly 
those  the  bases  of  which  are  the  tonic  (z.  e.,  C in  the  scale 
of  C)  and  the  dominant  (z.  e.,  G in  the  scale  of  C).  More- 
over, according  to  the  conventionalities  of  music,  when 
we  come  to  a final  cadence,  the  order  of  the  succes- 
sion of  the  fundamental  bass  notes  which  causes  the 
cadence  to  be  satisfactory  to  the  ear,  is  from  the  dominant 
(g)  to  the  tonic  (c)  above  it  and  not  to  the  C below  it ; i.  e., 
to  c,  representing  g : c,  or  the  ratio  3 : 4,  and  not  to  C, 
representing  C : g,  or  the  ratio  2 : 3.  Next  to  the  chords 
of  the  tonic  and  the  dominant,  the  most  important  chord, 
in  fact  the  only  one  that  is  important,  as  will  be  seen  by  a 
glance  at  the  music  on  page  343,  is  that  of  the  sub-domi- 
nant (z’.  e.,  of  F in  the  scale  of  C).  But  the  second  bar  of 
the  music  on  page  341  will  show  that  C is  related  to  F 
exactly  as  G is  related  to  C,  C being  the  dominant  when 


400 


PROPORTION  AND  HARMONY. 


F is  the  tonic,  just  as  G is  the  dominant  when  C is  the 
tonic.  Here  again,  then,  we  have  as  the  basis  of  harmony 
in  this  chord  of  the  sub-dominant,  the  ratios  either  of  2 : 3 
or  of  3:4.  But  the  importance  of  the  sub-dominant,  as 
every  one  acquainted  with  modulation  in  music  knows 
(see  Chapter  XV.  of  “ Rhythm  and  Harmony  in  Poetry  and 
Music”),  is  owing  to  the  fact  that  it  may  be  the  tonic  of 
a key  whose  dominant  is  the  same  note  as  the  tonic  of  itself 
when  the  subdominant.  We  may  say,  therefore,  that  here, 
too,  for  the  same  reasons  as  were  advanced  above,  the 
important  ratio  is  3:4,  though,  of  course,  considered 
merely  as  a factor  of  a scale  in  which  the  relation  of  the 
dominant  to  the  tonic  were  represented  by  3 -.4,  the  rela- 
tion of  the  sub-dominant  to  the  tonic  would  be  repre- 
sented by  2 : 3.  In  the  earliest  music  only  two  of  these 
chords — either  the  dominant  with  the  tonic,  or  the  sub- 
dominant with  the  tonic — were  used  in  order  to  harmonize 
all  the  notes  of  their  more  limited  musical  scales,  and  even 
now  it  is  possible,  though  not  customary,  to  harmonize  thus 
all  the  notes  of  our  scale ; because  the  tones  of  the  tonic 
and  the  dominant,  as  also  of  the  tonic  and  (excepting  the 
pitch  for  b or  si)  the  sub-dominant,  taken  together  repre- 
sent all  the  notes  of  the  scale,  being  composed  of  partial 
tones  that  contain  them  all.  See  the  music  on  page  341. 
In  the  same  way  the  complementary  colors  represent  all 
the  colors,  because,  taken  together,  they  are  compounded 
of  them  all.  See  page  331.  Once  more,  the  chords  of 
the  tonic  and  the  dominant,  or  of  the  tonic  and  the  sub- 
dominant, though  related,  appear,  when  alternating  in 
succession,  to  be  sharply  contrasted.  In  fact,  they  are 
the  chief  sources  from  which,  in  perfect  consistency  with 
unity,  all  those  modulations  are  developed  which  insure 
musical  variety.  (See  “ Rhythm  and  Harmony  in  Poetry 


COLOR-SCALES. 


401 


and  Music,”  Chapter  XV.)  Similarly,  complementary 
colors,  while  related,  are  also  contrasting  colors. 

Having  said  all  this,  it  is  now  to  be  added  that  there 
is  good  reason  to  believe  that  the  relation  between  the 
vibrations  of  complementary  colors  may  be  expressed  by 
the  same  ratio  as  that  between  those  of  the  dominant  and 
the  tonic  above  it,  namely,  3 : 4.  This  good  reason  is 
that,  although  the  slightest  change  in  a hue  makes  an 
apparently  great  change  in  the  numbers  of  its  vibrations, 
yet  notwithstanding  this  fact  the  calculations  that  have 
been  made  for  the  hues  supposed  to  represent  the  colors 
that  are  exactly  complementary,  very  nearly  represent  the 
exact  ratio  for  which  we  are  looking.  It  may  be  asked 
why  we  should  content  ourselves  with  this  result- — why 
we  should  not  examine  the  complementary  colors  pro- 
duced from  light  as  explained  on  page  331,  and  expect  to 
find  them  representing  this  ratio  not  very  nearly  but  ex- 
actly. One  answer  is  that,  where  waves  are  so  minute  as 
are  those  of  color,  it  is  hardly  conceivable  that  the  nar- 
rowest prism  should  divide  the  rays  in  such  a manner  as 
not  to  cut  off  entirely  some  of  the  light,  and,  therefore, 
as  not  to  change  the  number  of  the  vibrations  causing 
each  of  the  two  colors  produced.  This  is  one  reason  why 
it  seems  necessary  to  content  ourselves  with  approximate 
measurements.  Wherever,  in  the  list  on  page  402,  the  num- 
bers of  vibrations,  according  to  Von  Bezold’s  scale,  do  not 
approximate  those  used  which  indicate  the  ratio  of  3:4, 
there  is  an  interrogation  mark.  There  should  be  consid- 
ered in  this  calculation,  too,  the  vibrations,  omitted  by  Von 
Bezold,  causing  extreme  red,  numbering  between  472  and 
392  trillions,  and  those  causing  extreme  violet,  numbering 
between  727  and  773  trillions.'  Here,  among  the  vibra- 

1 It  may  be  interesting  to  compare  with  these  figures  those  given  by  Sir 
26 


402 


PROPORTION  AND  HARMONY. 


tions  causing  colors,  are  those  that  would  represent  the 
ratio  3:4:  See  Fig.  127,  page  334. 


Number  of  Tril- 
lions of 
Vibrations. 

Ratios. 

Carmine-red 

472 1 

Bluish-green 

630  [ 

3 : 4 

Vermilion 

480 ) 

ti 

T urquoise-blue 

640  j 

Orange  or  Vermilion 

491  1 

It 

Turquoise-blue 

655  f 

Orange  (?) 

500  ) 

4t 

Ultramarine  (?) 

666  f 

Yellow  (?) 

540  ) 

«< 

Bluish-violet  (?) 

720  s 

Yellowish-green 

560  l 

1 1 

Violet 

746  j 

Green 

580  | 

Purple 

773  f 

It  will  be  noticed  that,  with  great  accuracy  for  num- 
bers so  enormous,  the  ratio  3:4  in  almost  every  case 


Thomas  Young.  They  are  as  follows  ; and  it  will  be  found  that  in  both 
columns  the  ratios  representing  the  complementary  colors  approximate  3:4: 


Breadth  of  Wave. 

Vibrations  per  Second. 

Extreme  red 

0000.266 

458,000,000,000,000 

Red 

0000.256 

477, 000 , 000 , 000 , 000 

Orange 

OOOO.240 

506,000,000,000,000 

Yellow 

0000.227 

535,000,000,000,000 

Green 

0000.21 1 

577, 000 , 000 , 000 , 000 

Blue 

0000. 196 

622,000,000,000,000 

Indigo 

0000.185 

658, 000, 000, 000 , 000 

Violet 

OOOO.I74 

699,000,000,000,000 

Extreme  violet 

0000.167 

727,000,000,000,000 

In  one  of  the  latest  books  on  this  subject,  “ Studies  in  Spectrum  Analy- 
sis,” by  J.  N.  Lockyer,  the  number  of  vibrations  causing  extreme  red  light 
is  given  as  392,000,000,000,000;  and  causing  extreme  purple  as  757,000,- 
000,000,000, 


COLOR-SCALES. 


403 


expresses  the  relationship  between  complementaries. 
Where  it  does  not,  the  boundary  lines  between  the  colors, 
as  between  yellow  and  orange,  for  instance,  are  exceed- 
ingly difficult  to  find  on  the  spectrum,  and  we  may  be  jus- 
tified in  doubting  the  computations  from  which  the  ratios 
have  been  derived.  According  to  any  view  of  the  sub- 
ject, it  is  remarkable  how  the  conclusions  drawn  from 
these  ratios  coincide  with  those  reached  by  Von  Bezold, 
through  an  entirely  different  method.  In  its  way,  too,  it 
confirms  the  trustworthiness  of  that  scale. 

Let  us  now  consider  the  chords  in  music,  that  are 
formed  by  combinations  of  three  notes.  As  shown  on 
pages  217  and  225  of  “ Rhythm  and  Harmony,”  the  most 
perfect  chord  of  this  kind  is  the  major  triad,  represented 
by  C,  E,  and  G of  the  scale,  or  by  do,  mi,  and  sol  of  the 
solfeggio.  The  ratios  between  these  notes  are  as  follows  ; 
do  mi  sol  1 In  these 

1 £ f S do  is  to  mi  as  4 : 5 and  to  sol  as  2 : 3. 

Let  us  apply  these  ratios  to  the  colors.  As  a result, 
we  get  the  very  triads  of  colors  which  we  have  already 
obtained  in  two  other  ways.  The  numbers  used  indicate 
tens  of  trillions,  with  fractions  below  these  either  not  con- 
sidered or  averaged.  45  for  extreme  red  is  taken  from  the 
computation  of  Young  given  in  the  note  on  page  401  ; 52 
for  orange-yellow  is  formed  by  taking  an  average  between 
orange  (50,  as  given  on  page  402)  and  yellow  (54);  and  60 
for  green  not  only  corresponds  exactly  with  Von  Bezold’s 
chart  (Fig.  127,  page  334),  but  is  a result  of  an  average 
between  green  (58,  as  indicated  on  page  402)  and  bluish- 
green  (63). 

Extreme  red,  45.  Yellow-green,  56.  Ultramarine,  67. 

Orange,  50.  Bluish-green,  63.  Purplish-violet,  75. 

Orange-yellow  (?),  52.  Turquoise-blue,  65.  Purple,  78. 

Vermilion,  4S.  Green,  60.  Bluish-violet,  72. 


404 


PROPORTION  AND  HARMONY. 


To  sum  up  the  results  obtained  by  comparing  the  num- 
bers of  vibrations  per  second  of  the  sounds  producing  the 
musical  chord  with  the  numbers  producing  the  colors  that 
harmonize,  we  find  that,  although  there  is  nothing  repre- 
senting the  proportion  1:2,  there  are  combinations  cor- 
responding to  2:3,  3:4,  and  4:5.  To  understand  the 
following,  recall  from  page  400  that,  in  any  scale,  lower 
do  (1)  is  to  fa  precisely  as  sol  is  to  higher  do  (£■),  i.  e.,  as  3 : 4. 


COLORS. 

SOUNDS. 

Pairs  (complementary) 

Triads  (making  white) 

do  1 
do  1 

mi  i (f) 

fa  f (*) 

sol  f (|) 

If  now  we  wish  to  add  a fourth  color,  and  desire,  in 
so  doing,  to  follow  out  the  analogy  of  music,  we  must  use 
a color  corresponding  to  the  seventh  si,  and  thus  in  the 
scale  of  colors  very  near  the  do.  This  would  cause  a 
selection  of  four  colors,  only  two  of  which  would  affect 
one  another  so  as  to  need  to  be  separated  in  the  way 
indicated  by  Von  Bezold.  See  page  393. 

One  objection  of  this  writer,  as  well  as  of  others,  to 
allowing  the  numbers  of  the  vibrations  producing  the 
colors  to  have  weight  in  determining  which  shall  harmon- 
ize, is  that  these  vibrations  are  too  minute  for  the  eye  to 
recognize  the  difference  between  the  numbers.  Those 
who  say  this  confuse  the  perception  of  an  effect,  which 
only  is  necessary  in  the  eye,  with  the  perception  of  its 
cause.  As  pointed  out  on  page  344,  the  eye  does  not 
need  to  recognize  the  cause.  When  the  forms  of  vibra- 
tions in  adjoining  organs  of  the  retina  coalesce,  as  they 
do  when  2 vibratory  movements  of  one  organ  occupy  the 
same  time  as  3 of  another,  or  3 of  one  as  4 of  another,  or 
4 of  one  as  5 of  another,  then  the  optic  nerves  experience 


COLOR-SCALES. 


405 


a pleasurable  thrill  or  glow,  arid  this  is  all  of  which  they 
need  to  be  conscious. 

Nor  is  there  anything  to  gainsay  the  supposition  that 
the  forms  of  vibrations  in  adjoining  parts  of  the  retina 
may  coalesce  even  when  they  are  not  related  to  one  an- 
other as  they  are  when  producing  the  complementary 
colors.  We  may  ascribe  all  that  we  know  with  reference 
to  these  colors,  including  both  successive  and  simultane- 
ous contrast  (see  pages  371  to  3 77)  to  physical  organs  so 
constituted  that,  when  external  waves  of  light  are  divided 
according  to  a ratio  of  3 : 4,  each  of  two  parts  into  which 
these  organs  are  correspondingly  divided  is  affected  in  a 
peculiar  way.  But  this  fact — if  it  be  a fact — need  not 
make  less  plausible  the  supposition  that,  when  the  divi- 
sions of  the  external  color-waves  are  related  not  only  as 
3 : 4 but  also  as  2 : 3 or  4 : 5,  they  may  cause  the  vibrations 
of  both  these  parts  taken  together  to  coalesce  with  those 
of  other  adjoining  organs,  and  thus  fulfil  other  conditions 
tending  to  render  complete  the  analogies  between  the 
color-waves  and  the  sound-waves  as  well  as  between  the 
physiological  effects  which  they  respectively  produce  in 
the  eye  and  the  ear. 


CHAPTER  XXIV. 


ADDITIONAL  ART-METHODS  CAUSING  COLOR-HARMONY. 

Dissonance  and  Interchange — Criticism  by  Sir  Joshua  Reynolds — Gradation 
— Suggested  by  Nature — Physiological  Explanation  of — Abruptness — 
Transition  and  Progress. 

A FEW  paragraphs  more  will  contain  everything  not 
yet  considered  that  needs  to  be  said  with  reference 
to  the  influence  upon  harmony  of  the  art-methods  men- 
tioned in  the  chart  on  page  3.  In  painting,  as  in  music, 
dissonance  is  the  occasionally  necessary  use,  when  repre- 
senting the  variety  that  is  found  in  nature,  of  discordant 
coloring  ; and  interchange  aided  by  gradation  harmonizes 
it.  Notice  what  Von  Bezold  says,  on  page  393,  of  the 
arrangement  of  inharmonious  colors  by  separating  them. 
In  Chapter  XV.,  page  214,  of  “ Rhythm  and  Harmony  in 
Poetry  and  Music  ” the  influence  of  interchange  is  shown 
upon  the  effects  of  musical  chords  and  keys  that  otherwise 
would  be  inharmonious.  Its  influence  in  painting  is  simi- 
lar. Various  colors  in  one  part  of  a picture,  that  corre- 
spond to  colors  in  another  part,  whatever  discordant  colors 
may  intervene,  if  these  be  not  side  by  side,  may  make  the 
whole  harmonious  through  interchange.  This  effect,  like 
that  of  balance  which  it  closely  resembles,  is  usually  con- 
sidered psychological.  But  it  is  not  wholly  so.  Like 
balance,  too,  it  may  be  explained  physiologically  on  the 
ground  that,  although  the  vibrations  in  the  retina  may 
not  absolutely  coalesce,  those  that  do  not  coalesce  are, 

406 


INTERCHANGE  IN  COLOR-HARMONY. 


407 


in  the  first  place,  separated  so  that  the  optic  nerve  is  as 
little  conscious  of  the  fact  as  is  possible,  and,  in  the  second 
place,  are  distributed  so  that  in  different  places  the  differ- 
ences between  forms  of  vibrations  are  the  same,  producing 
a general  effect  of  likeness  in  methods  of  contrariety 
which  compensates  in  the  same  way  in  which  balance 
always  does,  for  a likeness  in  more  essential  regards. 

Just  how  it  does  this  is  well  brought  out  in  the  follow- 
ing criticism  on  the  “ Bacchus  and  Ariadne”  of  Titian.  The 
criticism  is  attributed  to  Sir  Joshua  Reynolds  ; though  the 
writer  does  not  recall  seeing  it  in  any  of  his  works.  But 
it  corresponds  with  something  to  the  same  effect  which  may 
be  found  in  his  “ Eighth  Discourse,”  and  is  worth  repeat- 
ing aside  from  its  source.  “ If  we  supposed  two  bits  of 
color  omitted,  namely,  the  red  scarf  of  Ariadne  in  the  up- 
per and  colder  portion  of  the  picture,  and  a blue  drapery 
on  the  shoulders  of  a nymph  in  the  lower  and  warmer  por- 
tion, it  would  leave  the  composition  divided  into  two 
masses  of  color,  the  one  hot  and  the  other  cold  ; the  warm 
portion  comprehending  the  reds,  yellows,  and  browns  of 
the  foreground,  and  the  cold  portion  comprehending  the 
blues,  grays,  and  greens  of  the  sky  and  trees ; and  this,  as 
in  the  rainbow  with  the  green  omitted,  would  be  produc- 
tive of  great  breadth,  but  it  would  be  destructive  of  union 
and  consequently  of  harmony,  for  it  would  leave  the  cold 
and  warm  colors  as  entirely  unconnected  as  though  they 
were  separate  designs  on  one  canvas.  To  correct  this,  and 
restore  the  union,  Titian  has  carried  up  the  warm  tints  of 
the  foreground  into  the  sky  or  cold  portion  of  the  picture 
by  means  of  the  red  scarf  on  the  shoulders  of  Ariadne, 
and  brought  down  the  cold  tints  of  the  sky  into  the  fore- 
ground by  the  blue  mantle  on  the  shoulders  of  the 
nymph  in  the  lower  or  warmer  portion  of  the  picture ; 


408 


PROPORTION  AND  HARMONY. 


and  thus,  by  dividing  the  painting  into  masses  of  warm 
and  cold  colors,  has  preserved  the  greatest  breadth  by  the 
opposition  of  warm  and  cold  colors  ; has  increased  their 
splendor  by  exchanging  those  of  one  side  for  those  of 
another,  as  just  stated  ; has  produced  union  and  har- 
mony; and,  at  the  same  time,  preserved  that  variety  so 
characteristic  of  nature’s  coloring.  Nor  is  this  all ; for  by 
a faithful  imitation  of  those  reflections  which  one  object 
throws  off  upon  another  in  its  immediate  neighbor- 
hood, and  by  that  balance  of  light  and  dark  colors  which 
gives  poise  and  symmetry,  and  by  that  tone  produced  by 
passing  a thin  transparent  color  over  the  entire  surface  (a 
process  called  glazing),  assimilating  and  softening  down 
the  most  opposite  tints  to 

“ ‘ Tones  so  just,  in  such  gradations  thrown, 

Adopting  Nature  claims  the  work  her  own,’ 

he  has  combined  in  one  design  all  those  excellent  quali- 
ties upon  which  depends  perfection  in  this  part  of  art.” 

As  interchange  separates  the  same  colors,  gradation , 
which  is  the  next  method  in  the  chart  on  page  3,  blends 
different  colors,  making  them  pass  into  one  another  by  im- 
perceptible degrees.  For  reasons  that  will  be  apparent 
without  explanation,  this  method  is  almost  necessarily  at- 
tendant upon  all  effects  of  principality , in  which  the  main 
color  needs  to  be  connected  with  the  subordinate  colors ; 
as  well  as  of  central-point  or  radiation , in  which  the  bright 
colors  are  connected  with  the  dull  ones,  and  of  massing,  in 
which  cumulated  colors  of  one  kind  are  connected  with 
surrounding  colors  of  other  kinds. 

The  necessity  for  gradation  is  suggested  by  nature. 
Owing  to  the  operation  of  light  and  shade  and  of  variety 
in  outline,  distance,  and  texture,  there  is  hardly  a square 


GRADATION  IN  COLOR-HARMONY. 


409 


inch  in  the  field  of  vision  in  which  the  colors  appear  to 
be  absolutely  the  same.  To  quote  from  Rood’s  “ Modern 
Chromatics”:  “One  of  the  most  important  characteristics 
of  color  in  nature  is  the  endless,  almost  infinite,  gradations 
which  always  accompany  it.  It  is  impossible  to  escape 
from  the  delicate  changes  which  the  color  of  all  natural 
objects  undergoes  owing  to  the  way  the  light  strikes 
them,  without  taking  all  the  precautions  necessary  for  an 
experiment  in  a physical  laboratory.  Even  if  the  surface 
employed  be  white  and  flat,  still  some  portions  of  it  are 
sure  to  be  more  highly  illuminated  than  others,  and  hence 
to  appear  a little  more  yellowish  or  less  grayish;  and  be- 
sides this  source  of  change,  it  is  receiving  colored  light 
from  all  colored  objects  near  it,  and  reflecting  it  variously 
from  its  different  portions.  If  a painter  represent  a sheet 
of  paper  in  a picture  by  a uniform  white  or  gray  patch, 
it  will  seem  quite  wrong,  and  cannot  be  made  to  look 
right  till  it  is  covered  by  delicate  gradations  of  light  and 
shade  and  color.  We  are  in  the  habit  of  thinking  of  a 
sheet  of  paper  as  being  quite  uniform  in  tint,  and  yet  in- 
stantly reject  as  insufficient  such  a representation  of  it. 
In  this  matter,  our  unconscious  education  is  enormously 
in  advance  of  our  conscious.  . . . Ruskin,  speaking  of  gra- 
dation of  color,  says:  ‘ It  does  not  matter  how  small  the 
touch  of  color  may  be,  though  not  larger  than  the  small- 
est pin’s  head,  if  one  part  of  it  is  not  darker  than  the 
rest,  it  is  a bad  touch.  . . . What  the  difference  is  in  mere 
beauty  between  a graduated  and  ungraduated  color  may 
be  seen  easily  by  laying  an  even  tint  of  rose-color  on 
paper  and  putting  a rose-leaf  beside  it.  The  victorious 
beauty  of  the  rose,  as  compared  with  other  flowers,  de- 
pends wholly  on  the  delicacy  and  quantity  of  its  color 
gradations.’  All  the  great  colorists  have  been  deeply 


4io 


PROPORTION  AND  HARMONY. 


permeated  by  a sentiment  of  this  kind,  and  their  works, 
when  viewed  from  the  intended  distance,  are  tremulous 
with  changing  tints — with  tints  that  literally  seem  to 
change  under  the  eye,  so  that  it  is  often  impossible  for 
the  copyist  to  say  exactly  what  they  are,  his  mixtures 
never  seeming  to  be  quite  right,  alter  them  as  he  will.” 

In  addition  to  the  principles  underlying  the  use  of 
gradation  derived,  as  thus  indicated,  from  the  presence  of 
it  in  nature,  there  is  evidently  another  derived  from  physi- 
ological conditions.  This  principle  is  that  changes  from 
one  form  of  color  to  another  should  usually  be  made  along 
the  line  of  least  resistance,  and  therefore  with  the  greatest 
gradualness.  Recall  the  application  of  this  principle  to 
curvature  on  page  292.  To  a certain  extent  gradation 
may  give  expression  to  the  same  physiological  conditions 
as  those  underlying  repetition  and  consonance.  The  play 
of  light  and  shade  upon  colors  does  not  necessarily  change 
their  hues,  and,  if  not,  it  does  not  change  the  form — only 
the  force — of  their  vibrations,  and  all  of  them,  if  already 
coalescing,  can  continue  to  do  so.  It  is  with  a recogni- 
tion of  how  largely  gradation  is  influenced  by  effects  of 
light  and  shade,  that  it  is  said  to  be  imperative  that  a 
dark  shade  of  a darker  color  should  always  be  put  with  a 
light  shade  of  a lighter  color,  and  not  the  reverse.  Light 
carmine,  we  are  told,  should  not  be  put  with  dark  ver- 
milion, but  dark  carmine  should  be  put  with  light  vermilion. 
Except  where  there  is  a combination  of  blue  and  violet, 
which  latter  is  darker  though  warmer  than  blue,  or  orange 
and  yellow,  which  latter  is  brighter  though  colder  than 
orange,  this  principle  requires  that  the  warmer  of  two  ad- 
jacent colors  should  always  be  the  brighter.  In  cases 
where,  as  in  these,  the  hue  as  well  as  the  degree  of  light 
is  changed,  the  eye  may  not  find  the  change  even  to  an 


GRADATION  IN  COIOR-HARMONY.  4II 

inharmonious  color  disagreeable,  if  it  takes  place  through 
imperceptible  degrees.  Our  senses  have  become  so  accus- 
tomed to  differences  of  this  kind  in  nature  that  they  ex- 
pect them,  as  it  were,  in  art.  Besides,  in  painting,  things 
that  are  very  nearly  allied  often  seem  to  be  alike,  just  as 
is  the  case  with  the  slight  variations  from  exact  require- 
ments allowable  to  rhythm,  rhyme,  and  the  notes  and 
chords  of  the  temperate  scale  now  used  in  music.  See 
pages  202  to  206  of  “ Rhythm  and  Harmony  in  Poetry 
and  Music.”  Physiologically,  the  explanation  of  grada- 
tion seems  to  be  that,  even  though  all  the  parts  of  the 
retina  do  not  vibrate  to  exactly  the  same  general  impulse, 
the  eye  does  not  experience  a disagreeable  sensation  in 
case  the  vibrations  of  the  parts  that  are  near  together 
differ  in  very  slight  degrees.  In  music,  graduated  differ- 
ences of  effect  take  place  in  time,  as  when  the  movement 
passes  from  one  key  to  another.  In  painting,  there  is  no 
reason  why  they  should  not  take  place  in  space,  and,  if 
they  do,  though  the  vibrations  in  one  part  of  the  retina 
may  not  coalesce  with  those  in  another  part,  the  eye,  for 
reasons  indicated  on  page  350,  may  be  hardly  conscious 
of  the  difference.  At  the  same  time,  as  a whole  scene  is 
usually  visible  to  a single  glance,  or  to  many  glances  con- 
stantly moving  from  one  to  another  part  of  the  scene,  it  is 
doubtful  whether,  in  case  the  changes  are  from  one  de- 
cided hue  to  another,  the  best  effects  of  harmony  can  be 
secured  by  gradation  without  the  aid  of  such  arrange- 
ments of  color  as  have  been  described  under  the  heads  of 
balance,  symmetry,  and  interchange. 

Notwithstanding  the  constant  application  in  art  of  the 
principle  of  gradation,  there  are  occasional  places  in 
which  one  color  needs  to  be  sharply  contrasted  with  an- 
other, and  this  necessitates  the  effect  termed  abruptness. 


412 


PROPORTION  AND  HARMONY. 


It  is  interesting  to  notice,  too,  that  while  gradation  tends 
to  a violation  of  the  law  of  consonance,  abruptness  tends  to 
its  fulfilment,  inasmuch  as  the  greatest  contrasts  are  really 
occasioned  by  the  proximity  of  the  complementary  colors. 
Abruptness  is  always  present,  for  instance,  when  an  object 
in  bright  light  is  placed,  as  is  frequently  the  case,  against 
its  own  shadow.  See  Fig.  102,  page  235.  In  Rem- 
brandt’s “ Woman  Accused  by  the  Pharisees,”  the  woman 
accused  is  robed  in  white  and  in  the  centre  of  the  chief 
light.  Her  accuser  stands  at  her  side  clothed  in  black. 
Of  course,  we  have  here,  necessarily,  the  greatest  possible 
contrast  and  abruptness.  But  evidently  this  does  not  in- 
terfere either  with  the  most  exact  fulfilment  of  the  princi- 
ples of  complement  and  consonance  or  with  the  most  delicate 
kind  of  gradation  used  as  a principal  and  general  method. 

Gradation  and  abruptness  together,  as  they  cause  one 
color  to  seem  to  change  and  to  pass  into  another,  produce 
the  effects  of  transition  and  progress.  With  these,  which 
need  merely  to  be  mentioned,  we  reach  the  last  of  the 
methods  of  composition  in  the  chart  on  page  3.  It  is  the 
combined  result  of  the  application  of  all  of  these  methods 
that  produces  the  general  effect  termed  harmony. 


CHAPTER  XXV. 


THE  FOREGOING  PRINCIPLES  AS  APPLIED  TO  DECORA- 
TIVE PAINTING. 

Differences  between  the  Use  of  Color  in  Pictorial  and  Decorative  Art — 
Differences  between  Classes  of  Forms  to  which  Colors  are  Applied  and 
Classes  of  Like  Colors  that  are  Applied  to  Like  Forms — Monochro- 
matic and  Polychromatic  Decoration — Color  on  the  Exteriors  of  Build- 
ings— Possibility  of  New  Styles  of  Architecture  in  our  Age — Modern 
Development  of  Mineral  Resources  and  Facilities  of  Transportation 
and  their  Influence  on  the  Shapes  of  Buildings — But  Especially  on 
their  Sizes  and  their  Colors  as  Produced  both  by  Pigments  and  by  the 
Materials  Used — Errors  to  be  Avoided  in  Attempting  Originality,  but 
Possibility  of  Success. 

''J" HE  most  of  what  has  been  said  with  reference  to  the 
harmony  of  color  applies  equally  to  pictures  and  to 
painting  as  used  in  architecture.  For  this  reason,  as  inti- 
mated at  the  beginning  of  this  discussion,  to  separate  the 
two,  when  treating  of  the  subject,  would  involve  an  un- 
necessary waste  of  time.  But  an  additional  chapter  seems 
to  be  in  place  here,  applicable — though  necessarily  in  only 
a very  general  and  superficial  way — to  decoration.  Decora- 
tive differs  from  pictorial  art,  primarily,  in  the  motive.  In  a 
picture,  color  is  used  in  order  to  reproduce  an  appearance 
of  nature.  In  decoration  it  is  used  for  its  own  sake. 
While  in  the  former,  therefore,  all  possible  shades  and 
tints  may  be  introduced,  so  long  as,  in  some  way,  they  can 
be  harmonized  ; in  the  latter,  those  only  ought  to  be 
introduced  that  in  every  way  must  of  necessity  har- 

413 


414 


PROPORTION  AND  HARMONY. 


monize.  Connected  with  this  difference  in  motive,  is  the 
same  difference  that  was  noticed  on  page  175  of  “ Rhythm 
and  Harmony  in  Poetry  and  Music  ” between  sounds  in 
speech  and  in  music.  In  the  one,  every  possible  degree 
of  pitch  may  be  used  ; in  the  other,  only  certain  degrees 
separated  from  one  another  by  decided  intervals.  Of 
course,  the  method  of  gradation  is  exemplified  both  in 
pictures  and  decoration  ; but  in  decoration  the  colors  used 
are,  as  a rule,  separated  from  one  another  by  more  de- 
cided intervals,  such  as  are  indicated  in  the  color-chart  on 
page  334;  and  they  are  more  apt  to  be  full  hues,  than 
light  or  dark  modifications  of  these,  such  as  are  gen- 
erally found  in  painting.  These  hues  are  placed,  some- 
times, side  by  side  ; but  they  produce  better  effects  when 
separated  by  black,  white,  gold,  or  silver  lines,  which  lessen 
the  influence  of  the  adjoining  colors  on  one  another. 
Moreover,  while  painting  deals  largely  with  the  greens, 
light  blues,  and  grays  predominating  in  the  world  about 
us,  decoration  shows  a large  use  of  the  reds,  oranges,  yel- 
lows, and  dark  blues,  as  if  one  design  of  it  were  to  produce 
contrasts  to  the  colors  seen  in  nature.  Again,  as  imitation 
of  form  or  outline  in  decoration  is  often  of  little  import- 
ance, almost  the  entire  effect  depending  upon  the  selec- 
tion and  arrangement  of  colors,  it  is  still  more  necessary 
than  in  painting  that  these  should  be  grouped  so  as  to 
fulfil  strictly  scientific  principles. 

Another  important  fact  recognized  in  decorative  art  is 
a difference  between  certain  classes  of  forms.  The  chief 
of  such  classes  are  mouldings  and  surfaces  ; and  of  these 
again  there  are  sub-classes.  Mouldings  may  be  straight, 
angular,  or  circular ; and  surfaces  may  be  large  or  small, 
and  shaped  in  many  different  ways.  It  is  a rule  in  deco- 
ration that,  in  the  same  composition,  like  classes  of  forms 


DECORATIVE  PAINTING. 


415 


should  exhibit  like  classes  of  colors.  In  order  to  aid  in 
securing  this  end,  the  colors  are  classed  as  follows:  first, 
black,  white,  gold,  and  silver;  second,  the  full  colors; 
third,  the  dark  colors ; and  fourth,  the  light  colors. 

Besides  this,  decorations  are  either  monochromatic  or 
polychromatic.  In  the  former,  different  shades  and  tints 
of  a single  hue  are  used,  separated  at  times,  however,  by 
black,  white,  gold,  or  silver.  In  the  latter,  all  the  hues  are 
used,  but,  as  a rule,  only  the  full  hues  ; and  in  case  a 
darker  or  lighter  effect  is  desired,  black  or  white  figures 
or  lines  are  placed  over  the  color.  This  method,  which 
probably  arose  at  a time  when  men  were  ignorant  of 
other  ways  of  producing  different  shades  and  tints,  is  now 
thought  by  some  to  be  the  only  way  in  such  kind  of  work 
of  producing  effects  of  unity. 

There  is  no  place  in  a treatise  like  this  for  extensive 
mention  of  the  various  modes  of  applying  color  in  the 
painting  and  furnishing  of  buildings.  There  is,  however, 
one  important  consideration  that  forces  itself  into  the  di- 
rect line  of  our  thought,  and  that  is  the  use  which  may 
be  made  of  color  upon  the  exteriors  of  buildings. 

It  is  often  urged  that,  in  our  age  and  country,  no  new 
style  of  architecture  can  be  originated.  With  reference 
to  this,  something  has  been  said  already  on  page  95  of 
“Art  in  Theory,”  on  pages  206  and  293  of  “ The  Genesis 
of  Art-Form,”  on  pages  330  and  406  of  “ Painting,  Sculp- 
ture, and  Architecture  as  Representative  Arts,”  and  on 
page  227  of  the  present  volume.  It  may  be  said  here 
that  probably  we  can  find  no  other  ways  of  bridging 
openings  made  for  doors  and  windows  than  those  which 
have  been  in  vogue  for  centuries,  and  which  have  already 
determined  the  chief  characteristics  of  the  Greek,  Roman- 
esque, and  Gothic  styles,  namely,  the  horizontal  lintel,  the 


41 6 PROPORTION  AND  HARMONY. 

round  arch,  and  the  pointed  arch,  and  that  probably  also 
the  necessity  of  securing  correspondence  in  architecture 
must  continue  to  cause  all  other  outlines  in  our  buildings 
to  resemble  these.  Yet,  while  this  is  true,  it  must  also 
be  true  that  in  every  period  in  which  there  is  progress, 
progress  is  possible  in  art. 

Our  own  age  has  made  an  advance  upon  all  preceding 
ones  in  two  regards  which  should  have,  and  already  have 
had,  some  influence  upon  our  architecture.  These  are  the 
development  of  our  mineral  resources  and  of  the  facilities 
of  transportation.  The  one  has  converted  iron,  together 
with  various  combinations  and  modifications  of  it,  into  a 
building  material,  and  the  other  has  lined  our  streets  with 
structures  of  stone  and  brick  exhibiting  every  variety  of 
color.  One  can  scarcely  believe  otherwise  than  that  if  one 
half  of  the  thought  expended  on  the  Parthenon  were 
expended  upon  incorporating  the  suggestions  and  possi- 
bilities derived  from  these  two  facts,  we  might  originate 
an  architectural  style  of  our  own  which  would  become  as 
classic  and  deserve  to  be  as  much  admired  as  that  of  the 
Greeks.  Iron  used  for  the  walls  of  buildings  is  inartistic. 
It  looks  like  an  imitation  of  stone  produced  by  wood  and 
paint,  while  it  is  standing;  and  it  cracks,  curls,  melts,  and 
ceases  to  stand  as  soon  as  a fire  of  any  magnitude  begins 
to  heat  it.  But,  used  for  roofs,  it  is  more  in  place,  and, 
where  so  used,  the  most  economical  and  convenient  shape 
that  can  be  chosen  for  it  is  often  the  most  beautiful.  A 
correspondence  between  its  arching  forms  and  like  forms 
in  the  stone-  or  brick-work  underneath  it,  might  give  rise 
to  a style  equally  novel  and  attractive. 

See  what  is  said  on  page  330  of  “ Painting,  Sculpture, 
and  Architecture  as  Representative  Arts,”  with  refer- 
ence to  methods  of  letting  iron  be  seen  in  ceilings.  Be- 


DECORATIVE  PAINTING. 


41 7 


sides  this,  iron  can  span  immense  spaces,  and  this  fact 
renders  the  columns  characterizing  the  Gothic  and,  to 
some  extent,  the  Greek  structures  as  much  out  of  the 
way  architecturally  in  some  of  our  modern  buildings,  as, 
with  our  modern  uses,  they  are  in  the  way  optically. 
Large  interiors,  however,  containing  few  or  no  columns, 
necessitate  very  artistic  treatment  of  the  wall-spaces. 
Otherwise,  everything  seems  too  airy  and  cold.  Arrange- 
ments of  mouldings  and  spaces  can  do  something  toward 
preventing  such  effects,  but  careful  attention  to  the  require- 
ments of  decorative  art  can  do  more.  Nor  in  such  cases 
should  efforts  be  confined  merely  to  painting.  Decorative 
color,  to  be  permanent,  should  be  resident  in  the  material 
used  ; and  here,  in  treating  both  exterior  and  interior 
walls,  architects  might  avail  themselves  of  our  modern 
facilities  for  transportation.  Pictures  have  been  made  of 
mosaics,  but  few  great  buildings  have  been  constructed  on 
the  principle  of  using  differently  colored  bricks  and  stones 
and  harmonizing  them  according  to  the  principles  of 
decorative  painting. 

Probably  an  architect  who  should  undertake  to  erect 
such  a building  would  be  considered  audacious  ; and,  un- 
less the  materials  and  colors  were  judiciously  chosen— not 
too  brilliant  or  diversified— and  were  arranged  in  strict 
fulfilment  of  the  principle  that  like  classes  of  forms  should 
be  characterized  by  like  classes  of  substances  and  hues,  and 
were  grouped  in  masses  large  enough  to  give  dignity  to  the 
effect — probably  the  result  would  prove  this  opinion  to 
be  correct.  Yet  a great  genius  might  produce  something 
with  a beauty  as  unique  and  successful  as  was  the  earliest 
Gothic  church  in  its  day,  and  surpassing  the  beauty  of 
most  of  our  buildings  as  much  as  the  frescoed  interiors  of 

the  present  New  York  merchants’  houses  surpass  the  white- 
27 


418 


PROPORTION  AND  HARMONY. 


washed  walls  of  their  Knickerbocker  ancestors.  Color  is 
certainly  an  element  of  beauty.  Why  should  it  not  be 
recognized  as  such  in  architecture?  Even  the  Greeks  ac- 
knowledged the  fact.  It  is  known  now  that  the  marble 
of  the  Parthenon,  unsurpassed  as  it  is  in  its  capabilities 
for  receiving  polish,  was  painted.  But  the  painting  has 
perished.  Used  on  exteriors,  it  always  does  perish.  Can 
no  imperishable  colors  be  used  thus  ? They  can.  In  a 
country  where  brick  and  stone  of  all  possible  compo- 
sitions and  colors  can  be  collected  from  all  quarters  at 
comparatively  slight  expense,  one  can  imagine  churches, 
halls,  streets,  entire  cities,  wholly  different  in  hue  and 
general  appearance  from  any  that  have  ever  existed, 
built  of  material  destined  to  remain  unchanged  as  long  as 
the  pyramids,  and,  for  a longer  time,  to  continue  to  be 
models. 


CHAPTER  XXVI. 


RECAPITULATION  OF  RESULTS  REACHED  IN  THESE  VOL- 
UMES ON  COMPARATIVE  ^ESTHETICS. 

Introductory  Statement — Examination  of  Facts  and  Opinions  in  “Art 
in  Theory” — Method  Adopted  in  Volumes  Following  it — In  “The 
Representative  Significance  of  Form” — Art  Developed  from  Natural 
Forms  of  Expression  — The  Methods  of  their  Development  — Ele- 
ments of  Representation  in  Arts  of  Sound,  as  Analyzed  in  “ Poetry 
as  a Representative  Art  ” and  in  “ Music  as  a Representative  Art” — 
As  Combined,  according  to  the  Same  Essays,  in  Poems  and  Musical 
Compositions  Considered  as  Wholes — Elements  of  Representation,  as 
Analyzed  in  “ Painting,  Sculpture,  and  Architecture  as  Representative 
Arts” — -As  Combined,  according  to  the  Same  Volume,  in  Paintings, 
Statues,  and  Buildings  Considered  as  Wholes — Form  in  General  as 
Treated  in  “ The  Genesis  of  Art-Form  ” — Form  in  Particular  as 
Treated  in  “ Rhythm  and  Harmony  in  Poetry  and  Music,”  and  in 
“ Proportion  and  Harmony  of  Line  and  Color  in  Painting,  Sculpture, 
and  Architecture” — This  Series  of  Volumes  Traces  All  Art-Develop- 
ments, whether  of  Significance  or  Form,  to  a Single  Principle — This 
Done  with  a Practical  as  well  as  Philosophic  Aim — The  Acknowledg- 
ment of  No  Standards  Leads  either  to  Imitation  or  Eccentricity  in 
Production  and  in  Critical  Judgment — The  Possibility  of  Finding 
Standards — These  Need  not  Interfere  with  Originality — Necessity  for 
the  Study  and  Knowledge  of  Standards  in  our  own  Age  and  Country 
— Unavoidable  Limitations  in  a Philosophic  and  Technical  Treatment 
of  the  Kind  Attempted  in  these  Volumes. 

PjNE  more  of  this  series  of  volumes  upon  Comparative 
Aesthetics  remains  to  be  published.  But,  accord- 
ing to  the  order  in  which  they  will  ultimately  be  arranged, 
this  is  the  concluding  volume.  It  seems  appropriate, 
therefore,  before  closing  it,  to  give  a brief  summary  of 


420 


PROPORTION  AND  HARMONY. 


the  results  that  have  been  attained,  together  with  suffi- 
cient references  to  the  methods  of  attaining  them  to 
render  what  is  said  intelligible. 

In  the  introductory  volume,  “Art  in  Theory,”  an  at- 
tempt was  made  to  derive  a true  conception  of  the 
requirements  of  art  from  a study  of  certain  facts  and 
opinions  concerning  it  acknowledged  by  all,  or  held  by 
writers  of  authority.  Guided  by  these  criteria,  nature 
was  first  distinguished  from  art,  and  then  the  lower  arts 
from  the  higher.  It  was  found  that  an  essential  charac- 
teristic of  these  latter  is  what  is  known  as  form,  but  in 
their  cases  a form  producing  always  two  apparently  dif- 
ferent effects,  one  derived  from  an  imitation  of  exter- 
nal phenomena,  and  the  other  from  a communication  of 
thoughts  and  emotions.  The  first  effect,  tending  to  em- 
phasize the  form  in  itself,  was  said  to  be  mainly,  though 
by  no  means  exclusively,  characteristic  of  classic  art,  and 
the  second  effect,  tending  to  emphasize  the  significance 
in  the  form,  was  said  to  be  mainly  characteristic  of  roman- 
tic art.  It  was  also  argued  that  the  emphasizing  of  either 
of  these  tendencies,  if  carried  so  far  as  to  involve  a neglect 
of  the  other  of  them,  is  fatal  to  artistic  excellence.  In 
indicating,  then,  the  conception  of  artistic  aims  best  tend- 
ing to  preserve  the  equilibrium  between  the  two  tendencies, 
it  was  pointed  out  that  art  neither  imitates  nor  communi- 
cates in  the  most  practically  effective  ways.  Because  aim- 
ing to  do  both,  its  chief  aim  cannot  be  to  do  either  the 
one  or  the  other.  Art  represents  natural  phenomena, 
as  one  may  say,  as  a means  of  representing  thoughts 
and  emotions.  Or,  to  express  this  differently,  art  empha- 
sizes representation,  developing  and  elaborating  the  fac- 
tors of  it  in  nature,  and  the  possibilities  of  it  in  the  mind. 
But  in  doing  this,  art  is  using  the  same  means  and  con- 


RECAPITULA  TION. 


421 


tinuing  the  same  modes  of  expression  as  those  that  are 
attributed  by  men  to  the  creative  and  divine  intelligence. 
The  impulse  to  art,  therefore,  may  be  considered  creative 
and  divine.  But  as  it  neither  imitates  nor  communicates 
in  the  most  usefully  effective  way,  we  must  trace  it  less  to 
the  useful  than  to  the  non-useful,  and  so  to  what  in  ele- 
mentary phases  is  called  the  play-impulse.  This  play- 
impulse,  even  in  dogs  and  kittens,  to  say  nothing  of  apes, 
tends  to  the  imitation  of  that  which  seems  interesting, 
attractive,  and  charming  in  one’s  surroundings.  The  same 
impulse,  when  turned  in  the  direction  of  art,  inasmuch  as 
this  always  involves  the  use  of  form,  tends  also  to 
imitation.  But  an  imitation  of  that  which  is  interesting, 
attractive,  and  charming  in  form,  especially  in  form  com- 
municating to  mind  and  spirit  the  suggestions  of  a crea- 
tive and  divine  impulse,  is  nothing  more  nor  less  than  a 
reproduction  of  what  men,  when  using  the  term  in  its 
highest  sense,  mean  by  beauty.  What  is  there  in  beauty, 
however,  that  it  should  be  used  by  the  art-impulse  when 
giving  expression  to  the  mental  and  spiritual  ? A review, 
which  follows,  of  the  history  of  opinion  on  the  subject, 
reveals  that  the  effects  of  beauty  are  well-nigh  universally 
attributed — not  always  explicitly  but  certainly  implicitly 
— in  part  to  form,  but  in  part  also  to  significance  sug- 
gested by  the  form.  In  other  words,  the  charm  exerted 
by  beauty  is  exerted  partly  upon  the  senses,  because  the 
elements  of  the  form  harmonize  with  one  another  and 
with  the  physiological  requirements  of  the  ear  or  eye,  and 
partly  upon  the  mind,  because  the  suggestions  of  these  ele- 
ments harmonize  with  psychological  requirements.  The 
consequent  definition  reached  is,  that  “ Beauty  is  a char- 
acteristic of  any  complex  form  of  varied  elements,  produc- 
ing apprehensible  unity  (z.  e.,  harmony  or  likeness)  of  effects 


422 


PROPORTION  AND  HARMONY. 


(i)  upon  the  motive  organs  of  sensation  in  the  ear  or  eye, 
or  (2)  upon  the  emotive  sources  of  imagination  in  the 
mind,  or  (3)  upon  both  the  one  and  the  other.”  There  are 
the  best  of  reasons,  therefore,  why  a creative  and  divine 
impulse  tending  to  imitation  should  reproduce  beauty, 
the  mere  existence  of  which  alone  may  involve  that  ap- 
peal to  the  mental  and  spiritual  nature  which  is  made  by 
what  we  term  significance.  But  we  must  not  forget  that 
in  art  the  mind  may  do  more  than  represent  significance 
as  a secondary  consideration,  as  would  be  the  case  did  it 
do  so  merely  because,  by  way  of  accident,  as  it  were,  a cer- 
tain significance  was  necessarily  suggested  by  the  form 
used.  The  mind  often  represents  thoughts  and  emotions 
as  a primary  consideration, — that  is,  it  decides  upon  them 
first,  and,  afterwards,  selects  the  forms  through  which  to 
communicate  them.  We  are  obliged,  therefore,  to  know 
something  about  the  ways  in  which  the  mind  communi- 
cates or  represents  thoughts  or  emotions  through  any 
forms  whatever,  irrespective  of  their  being  characterized 
by  beauty.  The  remainder  of  the  book  shows  how,  at 
different  stages  of  the  influence  exerted  by  precisely  the 
same  external  phenomena,  entirely  different  phases  of 
conscious  thoughts  and  emotions  are  aroused  to  activity. 
This  activity  is  analyzed  into  that  which  primarily  is 
instinctive  or  spontaneous,  is  reflective  or  responsive,  or 
is  a blending  of  both  the  others  in  what  may  be  termed 
the  instinctively  reflective  or  the  emotive.  It  is  shown  that 
for  every  phase  of  activity  there  is  only  one  natural  form 
of  expression  ; and  that  it  is  this  form  and  no  other  which, 
when  artistically  developed,  i.  e .,  developed  with  reference 
to  beauty,  finds  appropriate  embodiment  in  one  of  the 
five  arts  of  Music,  Poetry,  Painting,  Sculpture,  or  Archi- 
tecture. 


RECAPITULA  TION. 


423 


In  the  volumes  following  “ Art  in  Theory,”  the  order 
of  thought  adopted  in  that  book  is  reversed.  Having  be- 
gun the  discussion  of  the  general  subject  by  observing 
forms  as  they  have  been  produced  by  art,  and  drawing  in- 
ferences from  them,  ending  with  the  final  inference  that 
all  are  necessarily  expressive  of  a certain  significance,  it 
seemed  natural  that  the  endeavor  in  subsequent  volumes 
to  determine  how  art  should  fulfil  the  requirements  in- 
dicated in  the  introductory  volume  should  start  with  sig- 
nificance, and  work  outward,  showing  what  different 
conceptions  it  is  possible  to  express  in  art,  and  how  these 
determine  its  form.  In  pursuing  this  line  of  thought,  the 
first  thing  to  do,  of  course,  was  to  examine  the  connection 
between  significance  and  form  in  general.  This  subject  was 
assigned  to  the  volume  of  the  series  not  yet  published,  and 
to  be  entitled  “ The  Representative  Significance  of  Form.” 
The  next  thing  to  do  was  to  examine  the  connection  be- 
tween significance  and  the  possible  forms  of  each  of  the 
different  arts  in  particular.  This  was  done  in  the  volume 
entitled  “ Poetry  as  a Representative  Art  ” ; also  in  that 
part  of  the  volume  entitled  “ Rhythm  and  Harmony  in  Poe- 
try and  Music  ” which  is  devoted  to  the  discussion  of  “Music 
as  a Representative  Art,”  as  well  as  in  the  volume  entitled 
“ Painting,  Sculpture,  and  Architecture  as  Representative 
Arts.”  Having  examined  the  methods  of  representing 
significance  through  form  in  general,  and  in  each  class  of 
forms  in  each  different  art  in  particular,  the  next  thing  to  do 
was  to  examine  form  in  itself,  that  is,  as  something  which, 
though  influenced  by  significance,  and  in  practice  always 
connected  with  significance,  may,  nevertheless,  for  the  pur- 
poses of  analytic  study,  be  considered  as  existing  apart 
from  anything  else,  and  as  developing  according  to  laws 
having  to  do  mainly,  if  not  solely,  with  that  which  per- 


424 


PROPORTION  AND  HARMONY. 


tains  to  the  appeal  to  the  senses.  Here,  in  analogy  to 
the  course  pursued  when  studying  significance,  attention 
was  directed  first  to  the  sources,  methods,  and  effects  of 
form  in  general.  This  was  done  in  the  volume  entitled 
“ The  Genesis  of  Art-Form.”  Next,  what  had  been  learned 
with  reference  to  form  in  general  was  applied  to  form  as 
manifested  in  each  of  the  arts.  This  was  done  in  the  two 
concluding  volumes  of  the  series,  “ Rhythm  and  Harmony 
in  Poetry  and  Music,”  and  “ Proportion  and  Harmony  of 
Line  and  Color  in  Painting,  Sculpture,  and  Architecture.” 
To  describe  the  contents  of  the  different  volumes  more  in 
detail,  “ The  Representative  Significance  of  Form  ” begins 
with  the  presumption  that  form,  even  as  it  exists  in  nature, 
always  represents  some  significance;  and  that  it  is  from  na- 
ture, therefore,  that,  directly  or  indirectly,  a man  derives,  in 
the  main,  the  conceptions  which  he  embodies  in  art.  The 
methods  of  deriving  such  conceptions  are  first  considered, 
and  then  it  is  shown  how  each  class  of  conceptions  may  be 
represented  in  each  of  the  different  arts.  Advancing  from 
that  which  is  more  elementary  to  that  which  is  more  com- 
plex, there  are  treated  in  this  way  the  conceptions  of  space, 
time,  existence,  matter,  movement,  force,  arrangement, 
operation,  method  of  operation,  organism,  life,  irhport, 
and,  finally,  of  the  infinite,  the  eternal,  and  the  absolute,  to- 
gether with  conceptions  of  truth  in  the  abstract  and  in  the 
concrete,  as  embodied  either  in  formulae  or  in  action.  In 
all  cases  it  is  shown  that  significance  and  form  necessarily  go 
together.  After  this,  the  different  emphasis  which  the  ways 
of  blending  the  two  give  to  the  one  or  to  the  other  is  shown 
to  distinguish  artistic  from  religious  truth,  and  also  from 
scientific  ; and  the  various  conditions,  methods,  and  pur- 
poses are  unfolded,  in  connection  with  which  develop- 
ment and  expression  are  given  to  each  of  the  three.  In 


RECAPITULA  TION. 


425 


accordance  with  the  distinctions  thus  made,  it  is  then 
pointed  out  that,  as  manifested  in  art,  the  basic  principle 
of  the  religious  tendency  prompts  to  the  instinctive,  spon- 
taneous, spiritual  subordination  of  form  to  significance, 
which  we  have  in  the  sublime  and  the  grand,  the  most 
artistic  expression  of  which  is  in  epic  art  ; that  the  basic 
principle  of  the  scientific  tendency  prompts  to  the  reflect- 
ive, responsive,  materialistic  equipoise  of  significance  and 
form,  found  in  the  picturesque  and  the  simple,  the  most 
artistic  expression  of  which  is  in  realistic  art ; and  that 
the  basic  principle  of  the  distinctively  artistic  tendency 
prompts  to  the  instinctively  reflective,  emotive,  and  ideal- 
istic subordination  of  significance  to  form,  found  in  the 
brilliant  and  the  striking,  the  most  artistic  expression  of 
which  is  in  dramatic  art.  The  same  three  respective 
tendencies,  considered  both  in  their  tragic  and  their  comic 
phases,  are  shown  to  be  at  the  basis  also  of  the  more  im- 
portant subdivisions  of  epic,  realistic,  and  dramatic  art; 
after  ample  illustrations  to  exemplify  and  confirm  which 
propositions,  the  book  closes  by  finally  indicating  as  de- 
veloped from  the  same  tendencies  certain  expressional  dif- 
ferences, as  well  as  correspondences,  between  the  arts 
of  Music,  Poetry,  Painting,  Sculpture,  and  Architecture. 

As  has  been  intimated,  the  next  thing  in  the  order  of 
the  development  of  the  thought  was  to  apply  the  principles 
so  far  unfolded  to  each  of  the  arts  considered  separately. 
In  treating  of  these  arts,  the  discussion  is  begun  by 
showing  that  it  is  natural  as  well  as  necessary  for  a 
man  to  express  his  thoughts  and  emotions  through  audi- 
ble or  visible  forms ; and  that  a certain  method  of  de- 
veloping these  forms  causes  them  to  be  artistic.  It  is 
shown,  besides,  that,  even  before  being  thus  developed, 
the  forms  are  all  of  them  methods  of  communicating 


426  PROPORTION  AND  HARMONY. 

thoughts  and  feelings  through  using,  for  this  purpose, 
certain  external  factors  which,  in  themselves,  are  devoid  of 
thought  or  feeling ; in  other  words,  that  artists,  owing 
to  an  application  of  the  principle  of  association  or  of  com- 
parison, reveal  operations  of  the  mind  through  employing, 
either  by  way  of  appropriation  or  reference,  the  physical 
phenomena  of  nature;  and  that,  for  this  reason,  we  can 
understand  the  arts  fully  only  so  far  as  we  consider  them 
as  representative,  on  the  one  hand,  of  mental  concep- 
tions, and,  on  the  other,  of  material  surroundings.  In  the 
volumes  devoted  to  this  subject,  therefore,  it  is  shown 
that  it  is  possible  for  every  natural  method  of  expression 
to  become  thus  representative,  at  times,  both  of  the  hu- 
man mind  and  of  external  nature.  The  elementary  factors 
of  expression  are  shown  to  be,  in  the  arts  of  sound,  into- 
nations and  words,  and,  in  the  arts  of  sight,  gestures, 
drawings,  carvings,  and  other  objects  made  by  hand.  From 
these  primarily  it  is  argued  that  form  in  representative 
art  is  developed.  The  ways  in  which  it  is  developed  are 
indicated,  first,  by  analyzing  the  methods  in  which  these 
factors  are  made  to  be  expressive,  and  observing  for  what 
phase  of  representation,  either  mental  or  material,  each 
phase  of  expression  is  fitted  ; and  later  by  observing  the 
general  effect  of  the  representation  produced  when  the 
methods  and  phases  are  combined  in  a completed  art-form. 

Expression  is  found  to  be  produced  through  different 
methods  of  using,  in  the  arts  of  sound,  duration,  force, 
pitch,  and  quality  of  tone,  and — respectively  corresponding 
to  these,  in  the  arts  of  sight — extension,  strength  of  line, 
hue,  and  mixture  of  hues.  It  is  from  these  methods 
that  we  derive  and,  as  affected  by  instinctive,  reflective, 
or  emotive  tendencies,  that  we  appropriate  for  repre- 
sentative purposes  such  effects  as  those  of  movement, 


RECAPITULA  TION. 


427 


pause,  accent,  versification,  metre,  tune,  tone,  and  other 
characteristics  of  rhythm  and  harmony  of  sound  ; and  such 
effects  as  those  of  size,  shape,  shading,  tinting,  and  other 
characteristics  of  proportion  and  harmony  of  line  and  color. 

In  the  volume  entitled  “ Poetry  as  a Representative 
Art,”  as  well  as  in  the  essay  on  “ Music  as  a Representa- 
tive Art,”  it  is  shown,  for  instance, — to  mention  only  a few 
particulars  as  illustrative  of  many  more, — that,  both  by 
way  of  suggestion  and  of  imitation,  solemnity,  gravity,  and 
dignity  are  represented  by  long  words  and  notes  caus- 
ing slowness  of  movement  as  contrasted  with  the  oppo- 
site ; that  self-assertion  and  vehemence  are  represented 
by  distinctness  of  accent  and  loudness  of  tone  as  con- 
trasted with  indistinctness  and  softness  ; that  conclusive- 
ness, decision,  affirmation,  and  satisfaction  are  represented 
by  downward  as  contrasted  with  upward  movements 
either  in  the  tunes  of  verse  or  of  song;  and  also  that 
feelings  like  fright,  amazement,  indignation,  contempt, 
horror,  awe,  surprise,  solicitude,  delight,  admiration,  and 
determination  are  each  represented  by  different  qualities 
of  tone,  whether  indicated  in  vowels  and  consonants  or 
in  musical  instruments. 

In  the  last  halves  of  the  essays,  both  on  poetry  and  on 
music,  the  elements  which  are  considered  separately  in 
the  first  halves  are  examined  as  representing  mental  con- 
ceptions or  material  surroundings  when  combined  in  com- 
pleted art-products,  the  purpose  being  to  bring  out 
clearly,  if  possible,  as  applied  to  both  theme  and  treat- 
ment, whether  plain  or  figurative,  the  distinctions  between 
the  poetic  and  the  prosaic,  the  musical  and  the  merely 
sonorous. 

In  an  exactly  analogous  way,  the  general  subject  is 
developed,  as  applied  to  the  arts  of  sight,  in  the  volume 


428 


PROPORTION  AND  HARMONY. 


entitled  “ Painting,  Sculpture,  and  Architecture  as  Rep- 
resentative Arts.”  First,  through  an  analysis  of  the  ele- 
ments of  visible  representation,  it  is  shown  that  large 
size  or  deep  shading  in  certain  features,  when  connected 
with  the  opposite  in  other  features,  suggests,  whether  in 
landscapes,  figures,  or  buildings,  either  conceptions  or 
surroundings  characterized  by  such  traits  as  heaviness, 
strength,  immobility,  influence,  or  nearness  ; and,  again, 
that  outlines  formed  by  the  continuity  of  curves,  and  also 
those  manifesting  irregularity,  suggest  the  normal  and 
natural  in  landscapes,  and  the  free  and  unconstrained  in 
figures,  whereas  straightness,  angularity,  and  regularity 
suggest  the  abnormal  and  artificial,  as  in  effects  of  vol- 
canic action  in  nature,  of  self-conscious  and  constrained 
action  in  men,  and  of  rectangularity  in  buildings  and  in 
most  other  human  constructions.  In  unfolding  this  sub- 
ject, the  principles  shown  to  underlie  other  forms  of  visi- 
ble representation  are  applied  to  a complete  system  of 
expressing  thoughts  and  emotions  through  the  shapes, 
postures,  gestures,  and  facial  movements  of  the  human 
body.  Following  this,  comes  a discussion  of  the  repre- 
sentative significance  of  the  different  colors. 

The  concluding  part  of  the  book  treats  of  the  repre- 
sentation of  mental  conceptions  and  also  of  material  sur- 
roundings in  compositions  as  wholes;  first,  in  landscape, 
portrait,  genre,  historic,  allegoric,  and  symbolic  painting 
and  sculpture,  and,  after  this,  in  architecture.  In  discuss- 
ing this  latter  art,  it  is  shown  that  the  constructive  con- 
ception, as  well  as  the  plan,  can  be  represented  in  the 
interior  and  exterior  of  a building;  and  in  a series  of 
illustrations  presenting  side  by  side  various  huts  and  tents 
as  constructed  by  the  natural  man,  and  columns,  pedi- 
ments, entablatures,  arches,  roofs,  and  spires  of  perfected 


RECAP1TULA  TION. 


429 


art,  it  is  shown  that  the  latter  are  developed  from  the 
former  through  a picturesque  and  statuesque  and,  in  this 
sense,  representative  motive. 

Having  observed  now  how  each  of  the  arts  is  expressive 
of  significance,  in  that  it  is  representative  both  of  mental 
conceptions  and  of  material  surroundings,  the  next  thing 
in  order,  as  indicated  on  page  424,  seemed  to  be  to  direct 
attention  to  the  subject  of  form,  considering  this,  first, 
as  related  to  art  in  general,  and  next,  to  each  art  in  par- 
ticular. Form,  as  related  to  art  in  general,  was  treated 
in  the  volume  entitled  “ The  Genesis  of  Art-Form.”  Tak- 
ing up  the  thread  of  thought  where  dropped  in  the 
previous  volume,  this  opens  by  examining  the  very  be- 
ginnings of  form  when  representing  significance.  The 
necessity  is  pointed  out  of  having  inaudible  and  invisible 
thoughts  or  emotions,  when  they  are  to  be  imparted  to 
another,  communicated  to  him  through  some  audible  and 
visible  medium.  Then  it  is  pointed  out  that  the  partic- 
ular method  in  which  they  may  be  thus  communicated 
in  art  is  only  one  of  many  similar  ways  in  which  the  mind 
is  obliged  to  use  material  surroundings.  It  is  recalled 
that  all  knowledge,  and  not  only  this,  but  all  understand- 
ing and  application  of  the  laws  of  botany,  mineralogy, 
psychology,  or  theology,  depend  upon  the  degree  in 
which  a man  learns  to  separate  certain  plants,  rocks, 
mental  activities,  or  religious  dogmas  from  others,  and  to 
unite  and  classify  and  name  them  ; and  that  it  is  classifi- 
cation which  enables  him  to  have  knowledge  and  under- 
standing of  the  materials  which  nature  furnishes,  and  to 
make  an  efficient  use  of  them.  It  is  maintained  that, 
while  science  classifies  facts,  and  philosophy  theories, 
art  classifies  forms  or  appearances  ; and  it  is  stated  also 
that  the  general  process  in  all  cases  is  the  same, — a pro- 


430 


PROPORTION  AND  HARMONY. 


cess  which  involves  an  application  of  the  same  princi- 
ples of  association  and  comparison  which  are  mentioned 
on  page  426  as  being  at  the  basis  of  all  earliest  attempts  at 
expression.  This  process  in  its  elementary  stages  is  a put- 
ting of  like  with  like.  If  the  factors  be  not  actually  alike 
in  form  the  process  involves  gathering  them  into  groups 
according  to  the  principle  of  mental  association  ; or,  if 
they  be  alike  in  form,  of  doing  the  same  according  to  the 
principle  of  comparison.  The  essay  maintains,  in  short, 
that  it  is  the  endeavor  to  produce  unity  of  impression  out 
of  the  variety  and  complexity  everywhere  apparent  in  na- 
ture, as  one  is  influenced  sometimes  by  the  requirements 
of  the  mind,  sometimes  by  those  of  nature,  and  sometimes 
by  both,  that  leads  to  the  different  methods  adopted  in 
art-construction,  the  whole  of  which  methods,  arranged 
in  the  order  of  their  logical  development,  are  indicated  in 
the  chart  on  page  3 of  the  present  volume. 

In  the  volume  entitled  “ Rhythm  and  Harmony  in 
Poetry  and  Music,”  as  also  in  the  present  volume,  this 
method  of  putting  like  with  like,  as  modified  by  the  condi- 
tions of  variety  everywhere  characterizing  the  materials 
with  which  art  has  to  work,  is  shown  to  be  at  the  basis  of 
all  the  different  developments  of  form  as  form  with 
which  the  art  of  our  times  is  acquainted.  Rhythm  and 
proportion  are  traced  to  effects  produced  by  a grouping, 
of  which  the  mind  is  conscious,  of  like  or  allied  measure- 
ments, or  multiples  of  measurements,  in  time  or  space; 
and  harmony,  whether  of  spoken  words,  of  musical  notes, 
of  outlines,  or  of  colors,  is  traced  to  a grouping,  of 
which  the  mind  is  not  conscious,  of  like  or  allied  meas- 
urements, or  multiples  of  measurements,  in  vibratory 
movements.  To  exemplify  the  truth  of  this  statement, 
as  evinced  in  every  detail  of  the  forms  of  these  arts,  has 


RECAPITULA  TIOAr. 


431 


necessitated  much  explanation  and  no  little  repetition. 
But  these  are  excusable  if  they  have  suggested  any  import- 
ant considerations  not  before  recognized.  For  instance, 
the  latest,  and  perhaps  the  best,  book  produced  in  our 
country  which  discusses  poetic  form,  is  developed  from  the 
same  limited  conception  of  it  indicated  in  the  definition 
of  Poe  in  his  essay  on  “ The  Poetic  Principle,”  namely, 
“ the  rhythmical  creation  of  beauty.”  No  one  would  say 
that  in  “Rhythm  and  Harmony  in  Poetry  and  Music” 
there  is  any  lack  of  thoroughness  in  the  treatment  of 
rhythm  in  poetry  or  of  its  various  applications  and  possi- 
bilities,— to  say  nothing  of  the  freshness  of  the  treatment, 
owing  to  the  circumstance  that  a year  before  the  book 
was  published,  the  scientific  investigations  that  suggested, 
perhaps,  the  most  important  conclusions  in  it  had  not 
been  made.  At  the  same  time,  no  one  can  read  that 
book  carefully  and  not  recognize  that  harmony,  too,  as 
distinctly  differentiated  from  rhythm,  plays  as  noteworthy 
a part  in  the  general  effects  of  poetry  as  in  those  of 
music;  that,  different  as  are  both  factors  and  effects  as 
used  in  poetic  and  in  musical  harmony,  nevertheless,  the 
methods  of  it  in  both  arts  illustrate  identical  principles. 
That  an  analogous  fact  is  true,  not  only  in  these  arts,  but 
also  in  painting,  sculpture,  and  architecture,  has  been 
shown  in  the  present  volume,  concerning  the  line  of 
thought  in  which,  however,  nothing  need  be  added  here. 

To  recapitulate  : in  these  volumes,  the  effects  of  form  in 
art  have  been  traced  to  a single  principle,  and  to  the  same 
principle  have  been  traced  the  effects  of  whatever  signifi- 
cance also  may  be  expressed  in  each  form.  All  art,  in  any 
of  its  manifestations,  has  been  shown  to  be  an  empha- 
sizing, through  a method  of  elaboration,  of  factors  taken 
from  one’s  surroundings,  which  are  used  not  only  in  art, 


432 


PROPORTION  AND  HARMONY. 


but  in  every  attempt  at  expression,  for  the  purpose  of  rep- 
resenting, by  way  of  association  or  comparison,  some- 
times these  surroundings  themselves,  and  sometimes  the 
thoughts  and  emotions  communicated  through  them. 
Moreover,  whether  we  wish  to  emphasize  the  factors 
themselves,  or  the  purpose  for  which  the  mind  uses 
them,  each  end  is  best  attained  by  putting,  so  far  as 
possible,  like  with  like  in  the  sense  of  grouping  features 
having  either  corresponding  effects  upon  the  mind,  i.  e., 
like  significance  ; or  corresponding  effects  upon  the  senses, 
i.  e.,  like  forms  ; or,  as  is  frequently  the  case,  corresponding 
effects  upon  both  the  mind  and  the  senses.  Stated  thus, 
the  principle  may  seem  very  simple  and  insignificant. 
But  any  one  who  has  read  the  volumes  of  this  series,  and 
observed  the  applicability  of  the  principle  to  all  possible 
effects  of  form  in  all  the  arts,  together  with  the  way  in 
which  analogous  effects  in  different  arts  have  been  corre- 
lated to  one  another  ; and  who  has  observed  also  the 
applicability  of  the  principle  to  the  mental  effects  of  art, 
whether  produced  by  the  grandest  generalizations  that 
can  broaden  thought,  and  the  profoundest  passions  that 
can  excite  emotion,  or  only  by  the  smallest  specific  accent 
of  a syllable,  the  measuring  of  a tone,  the  shading  of  a 
line,  or  the  turning  of  a little  finger, — any  one  who  has 
observed  these  facts,  and  is  at  all  appreciative  of  the  vast- 
ness and  complexity  of  the  subject,  or  is  acquainted  with 
the  chaotic  conditions  in  which  the  histories  of  opinions 
have  left  men’s  common  conceptions  of  it,  or  is  merely 
aware  of  that  which,  in  general,  is  the  distinctive  aim  of 
all  philosophical  analysis, — any  such  man  will  recognize  the 
degree  in  which,  when  the  elements  investigated  are  made 
to  seem  single  and  simple,  the  comprehensiveness  and 
importance  of  the  discussion  are  enhanced. 


STANDARDS  OF  ARTISTIC  JUDGMENT.  433 

In  any  study  of  art,  however,  it  must  always  be  borne 
in  mind  that  to  reach  a philosophical  result  is  not  the  sole 
or  the  chief  aim.  This  aim  is  practical  ; and  it  was  a 
practical  aim  that  first  suggested  this  series  of  volumes. 
At  a time  when  their  writer  was  an  author  and  a teacher, 
looking  for  guidance  and  finding  none,  most  of  the  criti- 
cism of  the  day,  whether  of  poetry,  painting,  or  architecture, 
revealed  an  absence  of  any  standards  of  judgment,  if  not 
a disbelief  in  the  possibility  of  their  existence.  Indeed, 
some  of  the  foremost  leaders  in  criticism  took  the  ground 
that  there  are  no  such  standards,  an  opinion  virtually 
maintained,  despite  all  protests  to  the  contrary,  in  what 
are,  perhaps,  the  freshest  and  most  suggestive  of  the 
books  on  aesthetics  that  have  been  produced  even  very 
lately. 

As  a result  of  having  or  acknowledging  no  standard, 
about  all  that  criticism  can  attempt  is  to  observe  a poem, 
a painting,  or  a building,  and  praise  it,  in  case  it  resembles 
some  other  product  of  a like  kind — say  by  a Tennyson,  a 
Corot,  or  some  Greek  or  Gothic  builder — which  has  been 
previously  praised  by  some  other  critic.  Judgments 
formed  according  to  this  method  either  exalt  imitation  in 
production  into  artistic  excellence,  as  well  as  imitation  in 
opinion  into  critical  acumen  ; or  else,  because  there  seems 
some  defect  in  such  conceptions,  they  confound  in  their 
search  for  the  opposite  of  imitation  the  indications  of  mere 
eccentricity  with  those  of  genuine  originality.  Meantime, 
the  art  either  imitative  or  eccentric  that  is  developed  by 
such  conceptions  continues  to  prove  satisfactory  to  men 
so  long  only  as  the  temporary  fashion  that  occasions  it  con- 
tinues in  vogue.  There  is  not  a library,  or  picture  gallery, 
or  street,  or  campus  of  any  size  in  this  country,  that  is  not 
filled  almost  to  overflowing  with  modern  compositions 

28 


434 


PROPORTION  AND  HARMONY. 


which  were  extravagantly  praised  by  the  foremost  authori- 
ties of  a few  years  ago,  but  which  to-day  are  acknowl- 
edged to  be  well-nigh  worthless  as  specimens  of  art; 
and  the  sorriest  feature  of  the  condition  is  that  this  race 
toward  worthlessness  is  still  going  on  between  many  upon 
whose  works  enormous  sums  of  money,  to  say  nothing  of 
undeserved  and  misguiding  laudations,  are  now  being 
lavishly  expended. 

So  long  as  the  author  of  this  series  of  volumes,  upon  the 
principle  of  “ Live  and  let  live,”  refrains,  as  he  has  always 
consistently  done,  from  personal  attacks  upon  artists  and 
critics  and  patrons  of  art,  to  some  of  whom,  in  his  own 
conceptions,  he  is  now  very  definitely  referring,  he  cannot 
be  rightly  accused  of  being  willing  to  attain  notoriety  in 
that  easiest  way  possible  in  our  own  age, — at  the  expense 
of  others ; even  if  he  cannot  expect  to  be  recognized  as 
one  who,  in  all  that  he  has  written,  has  been  mainly 
anxious  to  be  helpful  to  them.  But  whatever  they  may 
think,  he  is  certain  that  he  will  prove  helpful  in  reality, 
in  case  he  succeeds  in  doing  no  more  than  directing 
attention  to  the  fact  that  the  conditions  of  art  that 
have  just  been  described  must  always  continue  so  long 
as  opinion  or  performance  is  based  upon  the  concep- 
tion that  there  can  be  no  approximately  definite  stand- 
ards. And  if  this  be  so,  it  is  not  being  theoretical 
but  practical,  to  maintain  that  in  art,  as  in  all  other 
departments  of  life,  these  standards  can  be  discovered. 
We  can  find  that  upon  which  everything  else  on  the 
earth’s  surface  rests,  if  only  we  can  get  down  deep  enough. 
We  can  find  the  basic  method  of  art,  if  only  we  can  do 
the  same.  To  find  this,  has  been  the  object  of  these 
volumes.  Nor  is  it  assuming  too  much  to  hope  that  the 
physiological  as  well  as  the  psychical  investigations  of 


STANDARDS  OF  ARTISTIC  JUDGMENT. 


435 


the  present  day  have  been  carried  so  far  that  no  further 
discoveries,  much  as  they  may  add  by  way  of  confirma- 
tion to  the  theories  here  unfolded,  will  necessitate  any 
material  change  in  their  general  trend. 

Another  thought  is  suggested.  The  tendencies  to  imita- 
tion on  the  one  side  and  to  eccentricity  on  the  other,  which 
have  been  said  to  characterize  the  developments  of  art 
where  there  is  no  belief  in  approximately  definite  stand- 
ards, is  connected  with  a false  conception  of  what  consti- 
tutes that  originality  which  everybody  acknowledges  to 
be  essential  to  great  art.  It  is  the  conception  that  origi- 
nality is  a constituent  of  mere  form.  Originality  of  course 
is  a characteristic  of  form,  in  which  alone  it  can  be  mani- 
fested ; but  the  artistic  originality  which  men  mean  to 
applaud  when  they  speak  of  it,  is  originality  of  form  as 
expressive  of  significance,  originality  that  is  felt  to  be  a 
manifestation  of  mental  freshness  and  uniqueness, therefore 
of  what  we  term— including  in  our  conceptions  both  the 
intellectual  and  the  spiritual — personal  force.  That  it  is 
this  force  issuing  from  the  sources  of  the  soul  to  which  men 
mean  to  refer  when  praising  originality,  needs  no  further 
proof  than  that  the  trait  which  they  praise  is  not  always 
prevented  by  imitation  of  form,  nor  always  helped  by  eccen- 
tricity of  form.  An  actor  can  show  his  personal  originality 
by  imitating  ; and  a very  bashful  man  can  entirely  hide 
his  by  eccentricity.  Notice,  too,  that  the  argument  against 
the  existence  of  standards  of  art  founded  on  the  supposi- 
tion that  they  may  interfere  with  originality  has,  for  the 
reasons  just  stated,  no  basis  in  fact.  To  make  external 
forms  conform  to  a standard  is  not  to  interfere  with  the 
expression  of  the  originality  which  is  of  the  soul  and  mind. 
Through  an  application  of  identical  methods, one  may  give 
an  elocutionary  education  to  two  men,  making  the  voices 


436 


PROPORTION  AND  HARMONY. 


of  both  equally  musical  and  their  movements  equally 
graceful.  Yet  the  method  as  carried  out  in  the  forms 
manifested  by  the  one  may  make  him  a great  and  original 
actor,  and  the  personality  behind  the  forms  manifested  by 
the  other  may  result  in  no  greatness  or  originality  what- 
ever. At  the  same  time,  the  first  man,  with  all  the  origi- 
nal bent  of  his  genius,  could  not  have  become  the  great 
artist  that  he  is,  without  learning  to  conform  his  repre- 
sentation to  the  standards  of  his  art.  Thus  it  is  in  all 
the  arts.  Criticism  cannot  produce  personality,  but  can 
guide  it  to  successful  performance.  It  can  prevent  that 
total  waste  of  ability  which  is  invariably  expended  upon 
worthless  products,  where  either  imitation  or  eccentri- 
city has  led  taste  away  from  a recognition  of  standards 
which  are  as  enduring  as  the  ages,  because  rationally  de- 
duced from  principles  deeply  seated  in  humanity  and  in 
nature.  Rules  of  art  cannot  create  artistic  ability  ; but 
they  can  cultivate  it.  They  cannot  make  a man  a genius ; 
but,  if  he  have  genius,  they  can  enable  him  to  give  it  vent 
in  such  ways  that  it  will  exert  its  due  influence  ; and,  if  he 
live,  as  every  man  does,  where  he  must  accommodate  his 
productions  to  the  demands  of  those  about  him,  the  study 
of  aesthetics  can  elevate  conceptions  and  tastes  so  as  to  give 
a higher  aim  to  the  efforts  which  are  directed  to  the  satisfy- 
ing of  them.  The  born  artist  may  be  a ruler  of  humanity 
by  divine  right ; but  it  is  art,  the  requirements  of  which 
can  be  taught  and  learned,  that  alone  can  give  him  his 
government,  army,  palace,  throne,  crown,  and  sceptre,  and 
not  only  these,  but  the  subjects,  too,  who  on  account  of 
their  appreciation  of  the  significance  of  these  will  acknowl- 
edge his  authority. 

That,  in  our  times,  these  requirements  of  art  need  to 
be  specially  pointed  out  and  dwelt  upon,  will  be  con- 


STANDARDS  OF  ARTISTIC  JUDGMENT.  437 

ceded  without  argument.  The  age  is  scientific,  and  the 
country’s  aims  are  directed  toward  material  progress. 
Both  facts  cause  us  to  emphasize  the  real  rather  than  the 
ideal,  the  substance  rather  than  the  suggestion,  that  which 
is  held  in  the  hand  rather  than  that  which  is  conceived  in 
the  brain.  In  such  conditions,  the  phase  of  the  play-im- 
pulse that  prompts  to  art  cannot  tend  to  give  expression  to 
its  highest  possibilities.  A cowboy  of  the  West  could  take 
little  pleasure  in  the  Seventh  Symphony,  the  “ Excursion,” 
the  “ Sistine  Madonna,”  the  “ Dying  Gladiator,”  or  Ros- 
lyn  Chapel  ; and,  for  this  reason,  no  artist  of  the  West- 
ern plains  would  be  stimulated  to  produce  its  like.  But 
taste  in  appreciation  or  production  can  be  cultivated  ; 
and,  in  the  degree  in  which  it  is  cultivated,  a new  realm 
of  thought  will  open  for  a man,  and  with  it  a recognition, 
hitherto  not  experienced,  of  those  almost  infinite  corre- 
spondences between  spiritual  and  material  relationships 
which  every  great  product  of  art  manifests.  Thus  gradu- 
ally the  mind  will  enter  a region  of  thought  in  which  the 
play-impulse,  which,  at  first,  is  satisfied  to  expend  its  ener- 
gies upon  the  merely  apparent  and  superficial,  will  care 
for  more  than  a fife  and  drum,  a jingle  of  rhyme,  a dash  of 
color,  a trick  of  chiselling,  or  an  incongruous  pile  of  stone 
and  mortar.  The  mind  will  not  be  satisfied  unless,  at 
times  and  often,  music,  poetry,  painting,  sculpture,  and 
architecture  suggest  the  profound  and  the  sublime  ; in 
fact,  unless  the  humanities  have  had  their  perfect  work, 
and  art  has  become  humanizing  in  all  of  its  relations. 

To  open  such  a region  to  the  mind,  has  been  the  object 
of  the  work  of  which  these  volumes  contain  the  records. 
The  region  has  been  explored  before;  but  of  late  years 
has  it  been  explored  in  the  right  way?  Historic  pro- 
ducts, simply  because  they  have  come  to  fill  a large  space, 


438  proportion  and  harmony. 

have  been  supposed,  though  often  only  weeds  and  under- 
brush, to  be  the  best  that  could  be  expected.  To  show 
that  this  is  not  so,  it  has  been  necessary  to  clear  obstruc- 
tions away  from  the  plants  of  better  promise  whose  prog- 
ress had  been  checked,  and  to  lay  bare  the  soil  where  sun- 
light and  nutriment  can  work  as  they  should.  To  spend 
one’s  hours  with  axe  and  spade  chopping  down  and  rooting 
up  is  not  wholly  satisfactory,  but  at  times  it  is  essen- 
tial ; and  this  fact  is  a sufficient  excuse  for  much  that  has 
made  the  records  of  this  work  dull  and  tedious,  requiring 
often,  no  doubt,  as  much  painstaking  care  to  read  them 
intelligently  as  to  write  them.  But,  perhaps,  the  student 
for  whom  the  work  has  been  done  will  prize  the  volumes 
the  more  for  their  own  practical  recognition  of  their  limit- 
ations. One  cannot  catalogue  the  implements  that  aid 
the  mechanism  of  technique  without  neglecting  rhyme 
and  rhythm.  He  cannot  beat  clear  recognition  into  minds 
and  senses  steeled  against  it,  without  a deal  of  reiteration. 
That  which  was  undertaken  in  these  volumes  did  not  seem 
to  permit  of  a method  that  might  have  proved  far  more 
pleasurable  both  for  author  and  for  reader.  How  can 
one  get  down  to  the  roots  of  anything,  so  long  as  he 
persists  in  making  his  chief  aim  the  enjoyment  of  its 
flowers?  Our  libraries  are  full  of  treatises  upon  art  ap- 
pealing to  the  imagination.  The  series  of  volumes  which 
this  concludes  has  been  intended  to  appeal  to  the  under- 
standing. We  may  exercise  imagination  and  go  astray,  in 
case  we  fail  to  exercise  the  understanding  also.  But  so 
long  as  we  are  really  using  the  latter,  whether  as  artists  or 
critics,  we  are  much  less  likely  to  go  astray,  however 
imaginative.  To  understand  a subject  completely,  one 
must  be  led  to  analyze  it,  and  to  perceive  its  minutest 
details.  Details  that  are  minute  require  minuteness  in 


CONCLUSION. 


439 


presentation.  Your  small  matter  may  be  as  effectually 
lost  in  generalities  of  style  as  a needle  in  a dust-heap. 
Or,  as  applied  to  considerations  of  a broader  character, 
one  cannot  manifest  the  coolness  needed  in  a philosophic 
presentation,  through  a manner  aglow  with  the  heat  of 
fancy  ; nor  accurately  balance  principles  in  the  scale  of 
argument,  when  allowing  either  side  of  it  to  be  borne  up 
or  down  by  a bias  of  sentiment.  This  work  on  aesthetics 
has  been  all  work  from  the  beginning.  Not  without  much 
conscious  expenditure  of  effort  and  constraint  has  the  au- 
thor been  able  to  the  very  end  to  hold  it  strictly  to  its 
own  province  and  purpose.  He  has  not  deviated  from 
these,  because  he  has  believed  that  both  for  himself  and 
his  readers,  both  for  the  critic  and  the  artist,  both  for  the 
producer  of  art  and  its  patron,  this  course  would  be  the 
surest  through  which  to  secure  the  desired  results.  And 
not  only  the  surest  but  the  shortest.  He  soonest  obtains 
leisure,  who  devotes  himself  most  exclusively  to  labor  in 
the  hours  of  labor.  He  soonest  enters  into  the  enjoy- 
ment of  the  garden  bright  with  its  fragrant  blossoms  and 
the  orchard  laden  with  its  ripening  fruit,  whose  days  of 
preparation  are  most  scrupulously  spent  in  clearing, 
weeding,  planting,  and  grafting. 


INDEX. 


Abacus,  considered  in  proportion 
as  a part  of  entablature,  203,  210, 
213,  215,  217,  221  ; defined,  185  ; 
depicted,  182;  measurements  re- 
lated to  breadth  of  column,  219- 
221  ; to  other  parts,  191-194,  195, 
198,  203,  205,  208-211,  213-215, 
217 

Abruptness — Art-Method,  3 ; of 
line,  67  ; of  color,  411,  412 
Accent,  6,  7 

Accuracy  of  measurements  de- 
termining ratios  in  art  not  es- 
sential, 179-181,  184,  185,  202, 
203 

Acropolis,  178,  224,  252,  257  ; Res- 
toration of  west  end  of,  186 
Acroterium,  183,  197 
^Egina,  temple  of,  182,  186,  189, 
192,  196,  204,  208-210,  212,  220, 
221,  224;  Temples  of,  and  of 
Bassae,  178,  196 

Aerial  Perspective,  colors  in,  321- 

324 

^Esthetic,  283  ; the,  vs.  the  ethical, 
108 

^Esthetics,  outline  of  system  of 
Comparative,  419-432  ; import- 
ance of  study  of,  436 
After-Image,  colored,  in  eye,  371, 
372,  375-377,  380-384 
Ageladas,  97 
Aglaophon,  300 

Agrigentum,  187,  191,  193,  195, 

221 

Aguilonius,  268 
Alexander  the  Great,  301 
Alexandrine  Greek  Art,  249 


Alliteration,  232 

Alteration — Art-Method,  3,  66  ; in 
color,  366 

Alternation— Art-Method,  3,  66, 

1 16,  127  ; in  architecture,  148, 
164-166,  168,  174  ; in  color,  361, 
369  ; in  outline,  231 

American  Face,  beauty  and  propor- 
tions of,  128,  129 
Angelo,  M.,  302 

Angles,  like,  as  determining  pro- 
portion, 66,  67 

Animals,  contours  elliptical,  288, 
289 

Ankles,  proportions  of,  132-134 
Anne,  Queen,  architecture,  227  ; 
poetry,  225 

Antiquities  of  Athens,  Stuart,  181 
Aosta,  Arch  of  Augustus,  at,  153 
Apelles,  92,  301 
Apollodorus,  300 

Apollo,  Belvedere,  83,  84,  98,  123  ; 
Sauroctonos,  99,  104,  141  ; 

temple  of,  at  Delos,  194,  221 
Apparent  effects,  important  in  art, 
243,  244,  258-264  ; in  propor- 
tional measurements  more  im- 
portant than  real,  iii.,  iv.,  24,  25, 
32,  34,  38,  151-161,  179,  180, 
217.  See  Perspective. 

Arcadia,  of  Pausanias,  26 
Architectura,  De,  Vitruvius,  26,  64, 

117,  120,  219,  256 
Architectural  Record,  243,  248. 
Architecture,  Antique,  de  la  Sicile, 

Hittorf,  182  ; History  of,  Fergus- 
son,  28  ; Principles  of  Athenian, 
Penrose,  29,  181,  248,  254,  262 


441 


442 


INDEX. 


Architecture,  5 ; colors  in,  and  in 
pictures,  296  ; colors  on  exteriors, 
189,  192,  194,  416-418  ; decora- 
tion in,  413-418  ; development 
and  progress  in,  227,  228,  415- 
418  ; Egyptian,  244,  249  ; en- 

tasis or  curves  in  straight  effects 
of,  234-265  ; Gothic,  64,  144-176, 
226,  227,  252  ; Greek,  8,  36,  64, 
177-228.  246-265  ; Greek  vs. 

Roman,  222-225,  262,  263  ; how 
made  artistic,  145-149  ; how  made 
representative,  145-148  ; irregu- 
larities in  Greek,  248-252  ; its 
relation  to  nature  and  to  imita- 
tion, 144,  145  ; judged  from  dis- 
tant effects,  35,  36,  179-1S1,  202, 
203,  244,  246,  249,  251,  265  ; per- 
spective in,  36,  234,  236-265  ; 
proportion  in,  40-42  ; proportion 
in  Gothic  and  modern,  56,  144- 
228  ; proportion  in  Greek,  177- 
228,  246-265  ; rhythm  of,  42,  184 

Architrave  in  Greek  temple,  182  ; 
proportion  to  frieze,  191-198  ; to 
other  members,  185,  186,  191, 
192,  194-196,  203,  205,  207,  209 

Aristodemus,  301 

Aristophon,  300 

Art,  anticipates  discoveries  of 
science,  298,  299  ; connection  be- 
tween significance  and  form  in, 
104-108,  1 12,  128,  129,  139,  140, 
420-432  ; creative  and  divine, 
421,  422  ; develops  with  scien- 
tific discovery,  299-308  ; influ- 
ence of  criticism  on  436,  437  ; not 
irresponsible  but  humanizing,  1 10- 
1 1 2 ; not  useful  but  pleasurable, 
421 

Art-Composition,  methods  of,  2 ; 
with  chart  of,  3 

Art  : Its  laws  and  the  reasons  for 
Them,  Long,  368 

Art  in  Theory,  2,  107,  129  ,297,  354, 
362,  415,  420,  423  ; analysis  of 
essay  on,  420-422 

Art  of  Painting,  Fresnoy,  122  ; 
Reynolds,  367 

Artemidorus,  301 

Arts,  as  expressive  of  phases  of 


mental  action,  422  ; of  time  and 
space,  4 ; of  sound  and  sight,  4-7 
Association,  as  influencing  concep- 
tions of  beauty,  104,  105,  107, 
129,290;  principle  of,  underly- 
ing art-development,  426,  430. 
432 

Assonance,  232 
Assyrian  Square,  type  of,  35 
Athenian  Architecture.  See  Archi- 
tecture. 

Athens,  temples  at,  249 
Atmosphere,  colors  of,  305,  306, 
319-324  ; to  be  distinguished 
from  local  colors  of  objects,  377- 

383 

Audran,  124 

Augustus,  Arch  of,  at  Aosta,  153 

Bacchus  and  Ariadne,  Titian,  407 
Backgrounds,  near  and  distant,  271- 
275,  278-282,  292,  293  ; colors  of, 
in  relief,  387,  388 
Bacon,  89 

Balance — Art-Method,  3,  63,  65,  78  ; 
in  architecture,  161,  171,  173-175  ; 
231,  284  ; in  color  and  painting, 
358-361,  364,  366,  367,  406,  41 1 
Barbizon-Fontainebleau  Painters, 
308 

Bassas.  See  Phygaleia. 

Baudry,  308 
Bavaria,  256 

Beautiful  in  Nature,  Life,  and  Art, 
The,  Symington,  298 
Beautiful,  the,  in  art,  421 
Beauty,  ascribable  to  association, 
104-108,  128,  290  ; to  effects  on 
mind,  107,  108,  318  ; to  physical 
causes,  113,  114,  361,  362  ; con- 
nected with  absence  of  visual 
effort,  282,  283  ; connected  with 
proportion  and  harmony,  2 ; curve, 
the  line  of,  59-61,  135,  136,  282, 
283,  286,  287  ; determined  by 
both  form  and  significance,  104- 
108,  112,  139,  140;  discrepancies 
in  standards  of,  112,  113  ; mean- 
ing and  office  of,  in  art,  421,  422  ; 
models  of,  from  nature  as  in  Greek 
art,  88-102,  hi,  140;  of  Ameri- 


INDEX. 


443 


Beauty — Continued. 

can  face,  128,  129  ; of  face,  126- 
129  ; of  human  form,  71,  101, 
104-108,  139,  140  ; vibrations  at 
basis  of,  1 13,  1 14 
Beauty,  Science  of,  Hay,  46 
Belgian  School  of  Painting,  304 
Bellini,  303 

Bezold,  Von,  ix.,  333,  387,  390, 
392,  401,  403,  404,  406 
Binocular  Vision,  266-295 
Birds,  elliptical  contours  of,  288, 
289  ; proportions  in,  78 
Black  and  White,  influence  on  com- 
plementary colors,  334,  335 
Blanc,  C.,  376 
Blouet,  182 

Blue  by  lamplight,  315  ; color,  in 
water  and  atmosphere,  318,  319. 
See  Colors. 

Bol,  305 
Boldini,  308 

Boris,  Tower  of,  in  Kremlin,  Mos- 
cow, 173 

Bouguereau,  308,  322 

Bow  Church  Steeple,  London,  171 

Breadth,  366.  See  Massing. 

Breton,  J.,  322,  354,  356,  360 
Brewster,  274,  282 
Brilliant,  colors,  objection  to  use  of, 
in  painting,  365,  385,  386  ; the, 
in  art,  425.  See  Colors. 

Brittany  Washerwomen,  Breton, 
354,  356,  360 

Broken  Colors,  304,  312.  See  Colors 
Brttcke,  274,  275,  282 
Buckhart,  J.,  255 

Cabanel,  308,  322 

Calf,  proportions  of  human,  132- 
134 

Camera,  21,  22 
Canal,  The,  by  Corot,  74-77 
Canterbury  Cathedral,  38 
Capital,  of  column,  as  related  to 
Greek  proportion,  185,  186,  1S8- 
191,  195,  198,  203,  207-210,  212, 
213,  217  ; considered  as  pendant 
of  entablature,  203,  207,  2x0  ; 
Corinthian,  220 ; Doric,  183  ; 
Ionic,  204  ; of  same  measurement 


in  Greek  temples  as  the  cornice 
and  stylobate,  188-191  ; propor- 
tional relationship  to  architrave, 
freize,  upper  width  of  column,  and 
width  of  metopes  and  triglyphs, 
191-195.  See  Abacus. 

Caracci,  303 
Caravaggio,  303 
Carlo  Dolci,  303 

Cathedral,  Canterbury,  38 ; Chi- 
chester, 41 , Ely,  52-56 
Central  Congregational  Church, 
Boston,  39 

Central  Point — Art-Method,  3,  64, 
65  ; in  color,  363,  368 
Ceres,  Temple  of,  Eleusis,  187,  194, 
221 

Cespedes,  De,  304 
Character.  See  Beauty,  Face,  Hu- 
man Form,  Significance. 

Chares,  98 

Chateau,  de  Randau,  51  ; Chenon- 
ceau,  53 

Chaucer’s  Crystal  Palace,  298,  299 
Chemical  action  in  nerves  of  seeing 
and  hearing,  382 
Chenonceau,  chateau,  53 
Chiaroscuro,  367.  See  Massing  and 
Light  and  Shade. 

Chiavavalle,  Dome  of,  Italy,  174 
Chichester  Cathedral,  41 
China,  art  of,  89 
Church,  an  American,  163 
Chlorophyl,  317 
Cimabue,  302 

Circles,  as  determining  proportional 
measurements,  68-72  ; especially 
when  intersecting,  136-139,  278- 
288,  291,  292.  See  Curves. 
Circumferences,  intersecting.  See 
Circles. 

Circumspective,  as  distinguished 
from  perspective,  233 
Claparede,  268 

Classic  vs.  Romantic  in  Art,  420 
Classification — Art-Method,  61,  429 
Claude  Lorraine,  305,  306 
Clothing,  ethical  influence  of,  108- 
112  ; proportional  divisions  of, 
79-84 

Cockerill,  19,  29,  44,  178,  181,  188, 


444 


INDEX. 


Cockerill — Continued. 

188,  189,  192,  196,  197,  204,  205, 
220,  248 

Cold  Colors,  303,  304,313,  320-324, 
384-388,  407,  408  ; in  aerial  per- 
spective, 321-324;  in  backgrounds 
and  reliefs,  387,  388  ; in  comple- 
mentaries,  335,  336,  384-388,  407, 
408  ; in-doors  and  out,  320,  321  ; 
in  shadows  at  different  times  of 
day,  319-321 

Cologne  Cathedral,  153,  155,  156, 
180,  207 

Colors,  action  of  eye  in  recognizing, 
378—383  ; actual  and  apparent,  24, 
243,  244,  318  ; actual  of  natural 
objects,  317-321  ; as  illumined  by 
other  colors,  314-322  ; as  imitated 
from  nature  in  painting,  243,  244, 
296-298,  389,  390,  414  ; as  repre- 
senting distance,  321-324  ; as  used 
by  Egyptian,  Greek,  and  later 
painters,  300-304  ; at  different 
times  of  night  and  day,  314-322  ; 
balance  of,  358-361,  364,  366,  367; 
bright  and  brilliant,  365,  374,  385, 
386  ; broken,  304,  312  ; compli- 
cation in,  369  ; congruity  in,  361, 
362,  368  ; consonance  in,  370-405  ; 
continuity  in,  361,  369  ; cold,  302 
-304,  313,  319-324,  335,  336,  384- 
388,  407,  408  ; dark,  311,  312, 
384-388  ; dull,  374  ; effect  of  dis- 
tance on,  243,  244,  321-324,  328, 
371  ; effect  of  light  and  darkness 
on,  311-313,  410;  effect  on  one 
another  when  side  by  side,  371, 
372,  384-396  ; English  School  of 
Water,  305;  full,  312;  gradationin, 
302,  303,  305,  306,  308,  406-412  ; 
harmony  of,  27,  326,  327,  353, 
355-418  ; high,  312,  374  ; in  paint- 
ing vs.  decoration  as  in  architec- 
ture, 296,  298,  389,  390,  413-415  ; 
light,  311,  312,  384-388;  local, 
312,  313,  325,  377-383  i low,  374  ; 
mixing  in  eye,  307,  337,  371  ; 
neutral,  313,  385,  386  ; on  ex- 
teriors of  buildings,  189,  192,  194, 
416-418  ; pale,  304,  312  ; pitch 
of,  6,  374  ; positive,  313  ; primary, 


313,  326  ; production  of,  from  light 
illustrated,  309-311,  329-331  ; 

production  of  from  pigments,  31 1, 
332,  333  ; quality  of,  6 ; scientific 
study  of,  necessary,  298-308  ; sec- 
ondary, 313,  326;  selected,  used 
in  art,  297,  312,  352  ; shades  of, 
3x2  ; shadows  of,  300,  303,  304, 
319,  320,  358,  361,  365-368,  376, 
378-380,  384-388,  390,  391,  408- 
412  ; theories  of  harmony  of,  326, 
327,  352-354,  391-405  ; tints  of, 
312  ; tone  of,  6,  308,  312,  327, 
355-358  ; transmit  and  reflect 
colors  like  their  own,  3 14-31 7 ; 
used  in  painting  for  color’s  sake, 
296,  297  ; varied  in  painting,  355, 
356,  365  I vibrations  of  retina, 
coalescing  to  form  harmony  of, 
347-351,  353,  354,  356,  373-375, 
377-383,  4°4,  405  J warm,  302- 
304,  313,  319-324,  327,  336,  384- 
388,  407,  408  ; waves  determining 
each  of  the,  402  ; waves  of,  in  the 
ether,  349,  350,  373—375,  377-383 
Color  Scale,  389-405  ; chart  of,  333 
-336,  390-393,  398,  402,  414 
Colossus  of  Rhodes,  98 
Columbus,  vi 

Columns  of  Greek  Temple,  184,187  ; 
breadth  to  height,  219 ; curves 
in,  260,  261,  262  ; flutings,  264, 
265  ; height  of,  less  than  apparent, 
151,  152,  202,  203  ; inter-spacing 
of,  195,  248,  263,  264 ; leaning 
of,  257,  258,259;  lower  diameter 
of,  196  ; proportion  of  height  of, 
as  related  to  entablature,  pedi- 
ment, tympanum,  and  stylobate, 
201-217 ; sizes  of,  248,  263; 
upper  diameter  of,  191-196  ; taper- 
ing of,  257,  259-263 
Common  Multiple  for  Vibrations 
causing  harmony  in  eye  or  ear, 
340,  343,  347,  353,  357. 

Common  Sense  as  applied  to  art 
subjects,  1 12 

Comparative  ^Esthetics,  sketch  of 
system  of,  419-432 
Comparison,  applied  to  measure- 
ment of  spaces,  10,  XI,  14,  24,  etc.; 


INDEX. 


44  S 


Comparison — Continued. 

Art-Method,  3,  10,  61-64,  6S  ; 
basis  of  color-harmony,  314-317, 
327-330,  354-360,  362,  364-368  ; 
basis  of  proportion,  14,  15,  19, 
23,  24,  28-43,  50,  52-56,  64, 
88,  116,  124,  134,  146,  162,  184; 
basis  of  rhythm,  ig,  23,  24,  etc.; 
principle  of,  underlying  art-devel- 
opment, 426-430,  432 
Complement — Art-Method,  3 ; in 
color,  297,  327-329,  354,  355,  412  ; 
in  proportion,  63,  68,  78,  173,  412 
Complementary  Colors,  basis  of  con- 
sonance, 370-377  ; basis  of  har- 
mony, 353-356  ; harmony  not 
always  produced  by,  335;  numbers 
of,  practically  infinite,  335,  397, 
398  ; production  of,  from  construc- 
tion of  the  eye,  viii.,  380-383; 
from  light,  vii.,  illustrated,  328- 
336 ; from  pigments,  332,  333  ; 
from  light  waves,  375-380.  See 
Contrast. 

Complexity — Art-Method,  3,  18,  61, 
146,  430  ; in  color,  328,  362  ; in 
proportion,  18,  61,  146  ; of  archi- 
tecture, 170,  171,  213,  216 
Complication — Art-Method,  3,66;  in 
color,  369  ; in  proportion,  170,  171 
Comprehensiveness — Art-M  e t h o d, 
3 ; in  color,  362,  363  ; in  propor- 
tion, 64 

Concord,  temple  at  Agrigentum, 
187,  193,  221 

Cones  and  rods  in  the  eye,  viii.,  349, 
350,  380-383 

Confusion — Art-Method,  3,  62  ; in 
color,  328 

Congruity — Art-Method,  3;  in  archi- 
tecture, 146-148  ; in  color,  361, 
362,  368  ; in  proportion,  64,  104  ; 
in  the  human  figure,  115,  116 
Conscious,  action  of  the  eye  in  per- 
ceiving outlines  of  different  shapes 
at  different  distances,  271-283; 
mental  action  when  making  meas- 
urements of  rhythm  and  propor- 
tion, iv. , v.,  23-27,  50,  64,  65, 
178,  179-  343.  344,  430,  431-  See 
Unconscious. 


Consonance — Art-Method,  vii.,  3, 
64,  66  ; in  architecture,  148,  166, 
168  ; in  color,  vii.,  351,  363,  370- 
405,  410,  412  ; in  outline,  231  ; re- 
sult of  proportional  ratios  in  vibra- 
tions, 343,  344,  394-405;  similarly 
produced  in  ear  and  eye,  372-377, 
394-405.  See  Harmony,  Ratios, 
and  Vibrations. 

Constable,  305 

Continuity — Art-Method,  3,  66;  in 
color,  361,  369 

Contour  of  human  form,  59,  68-72, 
85-87,  I35_143,  290-295.  See 
Elliptical,  Human  Form  and 
Shape. 

Contrast — Art-Method,  3,  63,  68, 
412;  in  color,  328,  329,  354-366; 
in  relief  from  background  of  color, 
387,  388;  simultaneous  in  color, 

376,  383,  386;  successive,  or  con- 
secutive in  color,  371,  372,  375- 

377,  383  ; analogue  of  successive 
in  sound,  372-374.  See  Comple- 
mentary Colors. 

Conversations,  Eckermann’s,  376 
Corinth,  temple  at,  195,  203,  255 
Corinthian  Order,  203,  220 
Cornelius,  306 

Cornice,  183,  186-196,  198,  201- 
207,  209,  212,  215;  like  measure- 
ment of,  and  of  Greek  capital  and 
stylobate,  188-191 
Corona,  182,  185-187,  190,  198,  203, 
205,  207-209,  2 1 3-2 1 5 
Corot,  308,  322,  433 
Correggio,  303,  304,  367 
Correspondence  between,  arts  of 
sound  and  sight,  1-7,  10  ; propor- 
tion and  harmony,  27,  31,  64-66, 
430,  431  ; proportion  and  per- 
spective, 20-31  ; proportion  and 
rhythm,  iv.,  v.,  vi.,  2,  3,  7,  10, 
13-19,  23-26  ; 74,  1 1 5-1 1 7,  179, 
430,  431  ; speech  and  proportion 
in  painting,  13-15,  74,  114-116; 
speech-harmony  and  harmony  of 
outline,  229-232,  431  ; speech- 
rhythm,  and  proportion,  13-15, 
7-i,  114-116.  See  Consonance, 
Harmony,  and  Proportion. 


44^5 


INDEX. 


Corti's  Rods,  347 
Countenance.  See  Face. 
Counteraction — Art- Method,  3,  62; 

in  color,  328,  392. 

Cranach,  306 

Creative  periods  early  in  art-history, 
222 

Criticism,  influence  of,  on  art  and 
originality,  436,  437 
Crystal  Palace  of  Chaucer,  298,  299. 
Culture,  influence  of,  on  art  and 
originality,  436,  437 
Curvalinear.  See  Curves. 

Curvature  as  related  to  proportion, 
141,  142.  See  Curves. 

Curved  lines.  See  Curves. 

Curves,  266-295;  causing  ease  of 
vision,  277-295;  comparative 
measurements  of,  in  columns,  262; 
exemplifying  gradation,  59-61, 
291-295;  in  human  bodies,  58-60, 
69-72,  134-142,  290-295;  in  archi- 
tectural straight  lines,  Egyptian 
and  Greek,  246-265;  in  horizontal 
straight  lines,  234-237,  239,  240, 
243,  257,  258;  in  vertical  straight 
lines,  237-239;  like,  as  determin- 
ing proportion,  58,  59,  62,  63, 
66-72,  78,  87,  134-142;  the  lines 
of  beauty,  282,  283 
Cymatium,  183,  191,  197,  198,  201- 
203,  206,  207,  212-214,216 
Cyma  Recta,  183-185 

Daedalus,  89,  97 
Damophilus,  300 
Dark  Colors,  311,  312,  385-388 
Daubigny,  322 
David,  306 

De  Architectura,  Vitruvius,  26,  64, 
117,  120,  219,  256 
Decamps,  322 

Decline  in  Art  after  periods  of  pro- 
gress, 222 

Decorative  Painting,  296,  298,  389, 
390,  413-418;  character  of  mediae- 
val, 301 ; distinguished  from  pic- 
torial, 296-298,  389,  33O,  9^3 
Delacroix,  306,  376 
Delagardetta,  181 
Delaroche,  306 


Delos,  temple  of  Apollo  at,  194, 
221 

De  Nittis,  322 

Descent  from  the  Cross,  the,  Rubens, 
358,  367;  picture,  359 
Diadumenos,  95,  97 
Diana,  temple  of,  at  Eleusis,  191, 
193,  221 
Diaz,  308 

Diseases  of  the  Eye,  Noyes,  2t 
Discobolus,  96,  97 
Dissonance — Art-Method,  3,  in  pro- 
portion, 66  ; in  colors,  406 

Distance,  as  represented  in  color, 
243,  244,  321-324,  366,  41  r ; 

effect  of,  on  eyes,  233,  234  ; pro- 
portions of  buildings  to  be  judged 
from,  iii. , 35,  180,  202,  244,  246, 
249,  251,  265  ; were  judged  thus 
by  Greeks  and  Egyptians,  244- 
259.  See  Perspective. 

Dolci,  C,  303 
Domenichino,  303 
Donaldson,  248 

Doric  Architecture,  181,  211,  219, 
220 

Dorotheus,  301 
Douw, 305 
Dove,  274,  275,  282 
Dramatic  Art,  425 
DuPiles,  122,  124 

Duration — Art-Method,  4-6,  16,  19 
Diirer,  306 

Dusseldorf  School  of  Painting,  306 
Dutch  Painters,  304 
Dyck,  Van,  304 
Dyke,  Van,  365 

Dying  Galatian,  or  Gladiator,  437 

Ease  of  eyes’  action  in  perceiving 
outlines,  139,  140,  230-233,  268- 
295 

Eccentricity,  cultivated  when  there 
are  no  standard  of  taste,  433,  434  ; 
versus  originality,  435,  436 
Eckermann,  376 
Edfou,  249 

Effect  of  distance  on  magnitude, 
light,  contrast,  and  detail,  Stim- 
son,  235 


INDEX. 


447 


Effects,  general,  as  from  distance, 
251,  252  ; optical.  See  Distance 
and  Illusions. 

Egyptian,  painting,  300  ; temples, 
244,  246,  249 

Elements,  of  Art  Criticism,  Samson, 
1 17;  of  Drawing,  Ruskin,  368 
Eleusis,  temple  of  Ceres  at,  194;  of 
Diana  at,  191,  193,  221 
Elgin,  Lord,  248 

Elizabeth,  Architectural  Style  of, 
227 

Ellipse,  280-291;  as  determining 
proportional  measurements,  68, 
69  ; in  form  of  vases,  plants,  birds, 
beasts,  fishes,  283-290  ; in  human 
forms,  137,  138,  290,  291,  295; 
illustrated,  287,  289;  its  extensive 
use  in  art,  283;  its  outline,  the 
line  of  beauty,  282,  283 
Elliptical.  See  Ellipse. 
Ellipticlanceolate  shape,  why  used 
in  art,  280-291 ; illustrated,  58,  59, 
70-72,  136,  137,  138,  280,  203- 
285,  289 
Ellis,  101 

Ely  Cathedral,  interior,  52-56 
English,  School  of  Water  Colors,  305 
Entablature,  in  Greek  temple,  183, 
187,  189,  192,  194-196,  198,  201- 
217,  221,  224,  245-252,  254-259; 
curvesin,  245-248,  254-259;  height 
as  proportioned  to  that  of  columns, 
pediment,  stylobate  and  tympa- 
num, 201-222 ; leaning  forward  of, 
245-250,  255-258.  See  Like  with 
Like,  Proportion,  and  Ratios. 
Entasis,  246-265.  See  Curves. 
Entombment,  The,  Titian,  366 
Epic  Art,  425 
Erectheum,  262 
Esculapius,  193 
Ethical  in  art-effects,  108 
Etty,  305 
Euphranor,  301 
Eupompus,  91,  300 
Eycks,  Van,  304 
Excursion,  Wordsworth,  437 
Experiment  at  basis,  of  Gothic  archi- 
tectural proportion,  252,  253;  of 
Greek,  252,  253,  265 


Expression,  elements  of,  in  art,  426- 
429  ; in  human  figure  as  a whole, 
93,  104-114,  128,  129,  139,  140. 
See  Beauty,  Face,  Human  Form 
Significance. 

Extension — Art-Method,  4-7,  19 

Exteriors  of  Buildings,  colors  of,  189, 
192,  194,  415-418 

Eyes,  action  of,  in  seeing,  139,  140, 
231-238,  257,  261,  263,  264,  286, 
291-295;  binocular  vision  of,  267-. 
295;  cavity  of,  22;  conscious  and 
unconscious  action  of,  in  perceiving 
outlines  and  relief,  271-275,  280- 
282;  Diseases  of,  21;  field  of  view 
of  both,  and  of  one  eye,  267-271, 
276-286  ; effect  on  perspective  of 
rotation  of,  237,  238;  formation  of 
image  in,  22;  mixing  of  colors  in, 
307 , 337,  37 r;  organism  perceiv- 
ing color,  349,  350,  380-383;  what 
secures  ease  of  action  of,  in  per- 
ceiving outlines,  139,  140,  230- 
233,  268-295 


Fabius,  301 
Fabullus,  301 

Face,  American,  128,  129;  beauty 
and  character  in,  105,  106,  128; 
conventional  character  of  Greek, 
92-95;  curvilinear  measurements 
of,  134,135;  expression  in,  94,  105, 
106,  128,  129;  Greek,  92-95,  125, 
126,  128,  129;  proportions  of,  85- 
87,  105,  106,  125-129;  rectilinear 
measurements  of,  85-87,  125-128 
Faun  of  Praxiteles,  97.  99 
Feet,  poetic,  16.  See  Measures. 
Fergusson,  J.,  28 

Field-theory  of  color-harmony,  353, 
354,  392 

Fillets,  Architectural,  187,  189,  203 
Finger  behind  another  as  seen  by 
one  and  both  eyes,  269 
Fishes,  elliptical  contours  of,  288, 
289  ; proportions  of,  78 
Flemish,  Correggio,  304  ; School  of 
Painters,  304,  305 
Florence,  Academy  of,  306 
Foliage,  real  colors  of,  317,  318 


44§ 


INDEX. 


Fontainebleau-  Barbizon,  School  of 
Painters,  308 
Force — Art-Method,  5-7 
Form  in  art,  considered  in  itself, 
429-432  ; two  effects  of  : com- 
munication and  imitation,  420- 
422  ; versus  significance,  104-108, 
112,  128,  129,  139,  140,  158,  420- 
432.  See  Contour,  Elliptic,  Hu- 
man Form,  Outline,  and  Shape. 
Fortuny,  308,  355,  365 
Foster,  M.,  267,  276,  345,  346,  347, 
_ 349 

Foundation.  See  Stylobate. 

Frere,  322 
Fresnoy,  122,  123 

Frieze,  Greek,  182,  185,  186,  igi- 
196,  205  ; as  related  to  archi- 
trave, column,  pediment,  and 
tympanum,  191-198 
Fromentin,  322 
Full  colors,  312 

Gainsborough,  305 
Ganymede,  statue  of,  103 
Genesis  of  Art-Form,  The,  1,  61, 
63,  64,  66,  67,  104,  117,  120,  146, 
168,  176,  232,  237,  286,  303,  328, 
329,  348,  358,  369,  415,  424,  429  ; 
analysis  of  argument  in  essay  on, 
429,  430 
Gentile,  302 

Geometric,  aesthetics,  295  ; designs, 
286,  287 

Geometry  in  proportion,  141 
German  Painting,  306 
Gerome,  308,  322 
Ghent,  street  and  belfry  at,  172 
Giants,  temple  of,  at  Agrigentum, 
191,  195,  221 
Giorgione,  303 
Giotto,  302 

Gladiator,  or  Galatian,  Dying,  437 
Glycon,  97 
Goethe,  92,  376 

Golden  Section,  as  determining  pro- 
portion, 27 

Good,  The,  in  art,  425 
Goodyear,  W.  H.,  243,  248,  249, 
255,  265 
Gorgasus,  300 


Gossip,  painting  by  C.  Marr,  355 
Gothic,  art,  227  ; cathedral,  64  ; ex- 
periments in  building,  252,  253  ; 
proportion  in,  52-56  ; revival  in 
architecture,  226 

Gradation — Art-Method,  3,  61,  67, 
408;  in  architecture,  148,  171-175; 
in  color,  302,  303,  305,  306,  308, 
406-412  ; in  human  face  and 
form,  138-140,  292-295;  phonetic, 
233 

Grammar  of  Painting  and  Engrav- 
ing, Blanc,  376 
Granet,  355 

Green  Color,  by  lamplight,  315;  dif- 
ficult to  paint  because  of  many 
complementaries,  335,  336;  living, 
in  landscapes,  318 

Greek, architectural  proportions,  1 17— 
228  ; architecture  as  contrasted 
with  Roman,  262,  263  ; conception 
of  proportion,  26-30,  44  ; conven- 
tional face,  92-95,  125,  126,  128, 
129,  134,  135  ; entasis,  246-265  ; 
experiments  in  methods  of  con- 
structing temples,  252,  253  ; fret, 
12  ; measurement  in  proportion 
apparent  not  real,  179-181  ; paint- 
ing, 300,  301  ; painting  of  exteri- 
ors of  temples,  189,  192,  194, 
416-418  ; proportions  of  human 
form,  117,  118,  120-124  ; study  of 
nature  in  producing  human  form, 
90-102  ; study  of  posture,  141, 
142  ; temples,  8,  64,  etc. 

Greuze,  306 
Gros,  306 

Grouping — Art-Method,  3 ; in  pro- 
portion, 61,  62,  67  ; in  color,  328 
Guido,  303 

Gwilt,  Joseph,  iii. , 120,  198 

Hadrian,  97 
Hals,  Franz,  305 
Hansen,  182 

Harmony,  Greek  use  of  term,  26,  27 
Harmony  of  Color,  2,  7,  325-412;  a 
human  invention,  297,  352,  353  ; 
andof  music,  similarly  conditioned, 
338-347,  372-377,  394-405;  and 
of  sound  analogous  vii. , 2,  7,  25-27, 


INDEX. 


449 


Harmony  of  Color — Continued. 
343-345  I as  related  to  consonance 
vii.,  35C  3/1  I as  tone,  327,  355- 
358  ; balance  in,  360,  361  ; con- 
nection of,  with  all  art-methods,  3, 
327-329,  357-359,  406-412;  cor- 
respondence between  causes  of, 
and  of  rhythm  and  proportion,  27, 
31,  65,  66,  343,  344,  430,  431; 
determined  by  ratios  between  rates 
of  vibrations,  347,  34S,  373-375. 
377_383,  394-405  ; determined 

by  vibrations  coalescing  in  retina, 
347-351.  354,  356,  373-375.  377- 
383,  404,  405  ; groups  of  two, 
three,  and  four  colors  producing, 
391-405  ; organs  of  eye  recog- 
nizing, 349,  350,  380-383  ; physi- 
ological basis  of,  iv. , v.,  338, 
347,  349-351,  353-358,  378-383, 
391-407, 430, 431 ; psychical  causes 
connected  with,  344,  360,  375, 
376,  406-408  ; theories  of,  326, 
327,  352-354,  391-405  : two  phases 
°f,  350-351  ; scales  of,  389-412  ; 
unconscious  action  of  mind  in 
judging  of,  iv.,  v.,  23-27,  64,  65, 
343-345,  404.  405 

Harmony  of  Outline,  23-26,  229- 
295  ; correspondence  to  harmony 
of  speech,  as  used  in  poetry,  229- 
232 

Harmony  of  Sound,  2,  7,  23  ; and 
of  speech,  26,  229,  230,  326  ; 
determined  by  ratios  between 
rates  of  vibrations,  and  physiologi- 
cal basis  of,  iv.,  v. , 23-26,  229- 
232,  338-348,  356-360,  398-400, 
403,  430 

Hay,  D.  R.,  28,  46,  49,  6S,  137, 
286-288 

Heat,  relation  of,  to  chemical  action, 
to  color,  and  to  nerve-perception 
of  particular  sounds  and  colors, 
382 

Hellquist,  363,  364,  366,  369 
Helmholtz,  vii.,  332,  340 
Hercules,  statue  of,  94,  97 
Hermes,  statue  of,  97,  100 
Hermogenes,  301 
High  colors,  312,  374 

29 


Hilarius,  301 

Historic  method  of  art-study  not 
always  the  best,  437,  438 
History  of  Painting,  brief,  300-308 
Hittorf.  182,  187-190,  193,  194,  197, 
208,  220 
Hofer,  248 
Hogarth,  305 
Holbein,  306 

Horizontal,  cornice  in  Greek  archi- 
tecture as  related  to  proportion, 
188,  189,  197,  203,  205-209,  215  ; 
level  in  perspective,  234-237,  239, 
240,  255,  256;  lines  in  perspec- 
tive, 234,  236,  238-243,  255,  256  ; 
made  aesthetically  effective  by 
means  of  curves,  234-237,  239, 
240,  243,  257,  258 
Horopter,  268,  269 
House  of  Fame,  Chaucer,  298 
How  to  judge  of  a picture,  Van 
Dyke,  365 

Flues,  312.  See  Colors. 

Human  Face.  See  Beauty,  Face. 

and  Human  Form. 

Human  Form,  beauty  of,  as  de- 
pendent on  association  and  signifi- 
cance, 92-108,  112-114,  128,  129, 
139,  140  ; on  likeness  in  measure- 
ments, when  clothed  or  unclothed, 
78-8S,  1 15-143  ; on  likeness  in 
vibrations,  113,  114  ; on  taste, 
113,  114,  128,  129  ; curvilinear 
outlines  of,  as  in  segments  of 
ellipses  and  circles,  58-60,  68-72, 
87,  1 34-143,  290-295  ; Greek 

measurements  and  proportions  of, 
120-130,  133,  134  ; proportions  as 
dependent  on  congruity  or  fitness, 
115,  116  ; on  curvilinear  measure- 
ments, 58-60,  68-72,  87,  135- 
143  ; on  rectilinear  measurements, 

78-88;  115-135 

Illusions,  optical,  in  connection  with 
sizes  of  columns,  263,  264  ; with 
straight  lines,  triangles,  and  cross 
lines,  240-249,  257,  258 
Image  on  the  retina,  21,  23  ; forma- 
tion of  this,  22  ; measurements 
of,  determine  measurements  of 
proportion,  23,  24,  34 


450 


INDEX. 


Imitation,  of  architecture,  224  ; of 
nature  in  color,  296-298,  352, 
414,  433,  434  ; in  criticism  and 
art-production,  433-436 
Impressionism,  extremes  of,  307 
Incongruity  — Art-Method,  3,  64; 
in  color,  362 

Individual  experience  and  experi- 
ment in  art-methods,  252,  253 
Induction,  method  of  practiced  be- 
fore time  of  Bacon,  89 
Inherent  Colors,  312,  313,  325 
Inness,  322 

Interchange — Art-Method,  3,  67  ; in 
architecture,  148,  166-168,  170, 
171  ; in  outline,  231  ; in  color, 
406-408,  41 1 

Interspersion — Art-Method,  3,  16  ; 
in  color,  368,  369 

Ionian  capital  and  order  of  archi- 
tecture, 203,  204,  219,  220 
Irregularity  in  Greek  temple-meas- 
ments,  248-250,  262,  263 
Israels,  322 

Italy,  painting  of,  302,  306 

Japan,  art  of,  89,  90  ; knowledge  of 
human  form,  90  ; lack  of  nude 
art,  no  ; morality  of,  no 
Jules  Breton,  354,  356 
Juno  Lucina,  temple  of,  at  Agrigen- 
tum,  187,  193 

Jupiter,  at  Nemea,  temple  of,  191, 
194,  221  ; at  Olympia,  temple  of, 
igo,  194,  221  ; Olympus,  temple 
of,  250,  262 

Kaffir  Station,  Africa,  34 
Karnack,  temple  at,  249 
Kaulbach,  306 

Keynote,  in  music  and  color,  357, 

358,  374 

Kuttenberg,  spire  at,  171 

Landscape,  proportion  in,  13,  14, 

73-78 

Laocoon,  98 
Lawrence,  305 

Le  Conte,  ix.,  21,  238  268,  272- 
275,  282,  349 


Leg  and  Foot,  proportions  of,  132- 
134 

Legh,  Peter,  27,  150 
Lens  of  Eye,  22  ; adjusted  to  differ- 
ent backgrounds,  273 
Leonardo  da  Vinci,  299,  302,  306 
Lerolle,  II. , 322,  361 
Lessing,  306 
Lesueur,  306 
Liberty,  Thompson,  219 
Life,  colors  of,  in  nature,  317-319 
Light  and  Shade,  abruptness  in, 
412  ; as  represented  by  early  and 
later  painters,  301-304  ; as  repre- 
sented in  different  colors  at  differ- 
ent times  of  night  and  day,  314- 
316,  319-324  ; balance  produced 
by,  358-361  ; complementary 
color  of  in  the  shadow,  376,  378- 
380,  384-388,  390,  391;  grada- 
tion in,  408-411  ; massing  in, 
366-369 

Light  colors,  311,  312,  384-388  ; 
light  tint  of  light-color  put  with 
dark  shade  of  dark  color,  and  vice 
versa , 410 

Light  in  general,  as  in  atmosphere, 
distinguished  from  local  color, 
377-383 

Like  with  Like,  basis  of  artistic 
classification,  61-67  note,  430- 
432  ; basis  of  proportion,  v.,  8, 

10-19,  39-43 ; 52-56,  59.  6°.  62- 
64,  68-84,  87,  88,  1 16,  1 1 7,  120- 
143,  184,  222  ; basis  of  harmoni- 
ous coloring,  314-317,  325-328, 
361,  362,  364-366,  368-370;  in 
measurements  of  Greek  abacus, 
corona,  and  other  mouldings,  185- 
188  ; of  Greek  capital,  cornice, 
and  stylobate,  188-191,  221  ; of 
Greek  architrave  frieze,  com- 
bined raking  cornice  and  cyma- 
tium,  upper  diameter  of  columns, 
and  of  metopes  and  triglyphs, 
191-195,  221  ; of  Greek  entab- 
lature, tympanum,  and  upper 
space  between  columns,  195- 
199,  221  ; of  Greek  entablature 
with  capital  and  pediment,  198, 
201,  202,  204-212,  221  ; of  human 


INDEX. 


451 


Like  with  Like — Continued. 
face,  85-87,  105,  106,  125-129; 
of  human  form,  58-61,  68-72,  78- 
88,  115-135  ; of  modern  archi- 
tecture, 51-58,  1 16,  117,  149- 

176,  225,  226;  of  landscapes,  13, 
14,  73-78  ; of  Greek  architecture, 
185-226  ; of  rhythm,  16-18,  64, 
65,  etc.  ; illustrated  in  poetry  and 
music,  16-18,  230,  231,  232  ; in 
ornamentation,  IT-13  ; in  recti- 
linear and  curvilinear  outlines, 
39-42,  52-59.  61,  64,  68-72; 
not  inconsistent  with  alternation, 
116,  117,  127  ; not  inconsistent 
with  variety,  62  note,  etc.  See 
Harmony,  Proportion,  Ratios,  and 
Vibrations. 

Lines,  curved,  indicating  likeness 
and  proportion,  58,  59,  62,  63, 
66-72,  78,  87,  134-142  ; imagin- 
ary, indicating  proportional  meas- 
ments,  85-88  ; poetic,  rhythm  of, 
18  ; straight,  indicating  propor- 
tion, 6,  7,  58,  68,  79,  80.  See 
Curves,  Horizontal,  Perspective, 
Proportion,  and  Vertical. 

Lippi,  302 

Lloyd’s,  W.  W.,  Appendix  to  Works 
of  Penrose  and  Cockerill,  19,  29, 
44,  183,  194,  196,  201,  202,  211, 
218 

Local  color,  312,  313,  325  ; as  dis- 
tinguished from  atmosphere,  377- 
383  ; as  perceived  by  eye,  377- 

383 

Locksley  Hall,  Tennyson,  18 
Long,  S.  P.,  368 
Loomis,  E.  IL,  ix. 

Lorraine,  305 
Ludwig  I.,  256 
Luxor,  249 
Lysippus,  91,  97,  98 

Maas,  305 

Maison  Carree,  245-247,  249  ; illus- 
tration of,  245,  247 
Manner  or  style  as  related  to  matter, 
438.  439  . 

Maori  Festival,  33 
Marquand,  A.,  ix 


Marr,  C.,  355 

Marriage  at  Cana,  Paul  Veronese, 
360 

Masaccio,  302 

Massing — Art-Method,  3,  66  ; in 
color,  364,  366-369,  408 
Measures  in  music,  16-18  ; in 
poetry,  16-19 

Measurements,  accuracy  of,  not 
essential  in  art,  179-181,  184,  185, 
202,  203  ; apparent  not  actual  at 
basis  of  proportion,  iii. , iv.,  24, 
25,  32,  34,  38,  39,  15 1,  179  ; con- 
scious of,  in  effects  of  rhythm  and 
proportion,  iv.,  v. , 23-27,  50, 
179  ; different  schemes  of,  in  dif- 
ferent parts  of  forms,  116,  117, 
127  ; natural  tendency  to  make, 
10,  11,  14;  to  join  like  with  like, 
10,  11,  14;  unconscious  of,  in 
effects  of  harmony  of  color  or 
sound,  iv.,  v.,  23,  26,  27,  343- 
345,  404,  405.  See  Like  with 
Like,  Ratios,  and  Proportion. 
Mediaeval  Castle,  36 
Medinet  Habou,  246,  249 
Meleagros,  statue  of,  102 
Memling, H. ; 304 

Memoir  on  The  Systems  of  Propor- 
tion, etc.,  Lloyd,  19,  44 
Memorabilia,  91 
Mengs,  R.,  306 
Mephistcpheles,  106 
Metopes,  12,  192-195,  214 
Michael  Angelo,  302 
Micon,  300 

Middle  Ages,  art  of,  89 
Millet,  J.  F.,  308,  322 
Milton,  21 1 

Mixing  of  colors  in  eye,  307,  337, 
371  ; in  pigments,  311,  332,  333 
Minerva,  statue  of,  97  ; temple  of,  at 
Sunium,  193,  221  ; at  Syracuse, 
193 

Models  in  art,  need  of,  88-102,  ill, 
140,141,144,  145  ; used  by  Greeks, 
88-102,  hi 

Modern  Chromatics,  Rood,  ix.,  315, 
321,  386,  393,  396,  409 
Modern  Painters,  Ruskin,  59 
Monks  in  Oratory,  Granet,  355 


452 


INDEX. 


Moorish  Art,  227 

Moscow,  Tower  of  Boris,  Kremlin, 
at,  173 

Mouldings,  architectural,  187,  igr, 
192,  197,  198,  208,  209  ; coloring 
in  Greek,  192 
Muller,  268 

Munich,  School  of  Painting,  306 
Murillo,  304 

Music  16,  17.  See  Consonance  Har- 
mony, Rhythm,  and  Proportion. 
Music  of  the  Eye,  Legh,  27,  150 
Myron,  97 

Natural  History,  Pliny,  91,  92,  301 
Nature,  Greek  study  of,  in  human 
figure,  82-102,  tii  ; imitation  of, 
in  coloring,  243,  244,  296-298, 
389,  390,  414  ; necessity  of  study 
of,  82-102,  hi,  140,  141,  144, 
145  ; proportion  in,  13,  14,  74- 
79  ; real  colors  of  objects  in,  3 1 7— 
322 

Nausica,  figure  from  Poynter,  142 
Nemea,  temple  of  Jupiter  at,  igr, 
194,  203 

Nemesis,  temple  of,  at  Rhamnus, 
187,  193,  221 

Neptune,  temple  of,  at  Psestum, 
187,  193,  221 

Netherlands,  painters  of  the,  303, 
386,  388 

Neutral  Colors,  313,  385,  386 
Newton,  309 
Nicias,  301 
Nicomachus,  301 
Nimes,  France,  245-249 
Niobe,  Statue,  Group  of,  98,  101 
Notes,  ratios  of,  in  music,  16  ; see 
Harmony,  Ratios,  Vibrations. 
Noyes,  H.  D.,  21 
Nude  Art,  109-112 

Olympia,  temple  of  Jupiter  at,  190, 
194,  221 

Olympus,  temple  of  Jupiter,  250, 
262 

On  the  Law  of  Proportion  which 
Rules  all  Nature,  Zeising,  27 
Opera  House,  Paris,  167,  170,  etc. 
Opie,  305 


Orcagna,  302 

Order — Art-Method,  3 ; in  propor- 
tion, 62,  1 16  ; in  color,  328 
Organic  Form — Art-Method,  3,  63, 
146  ; in  color,  358,  360,  363 
Organ  Recital,  Lerolle,  361 
Originality,  not  inconsistent  with 
standards  of  art  and  criticism, 
433-  435,  436 

Ornamental  Geometric  Designs,  etc. , 
Hay,  286 

Ornamentation,  based  on  principle 
of  putting  like  with  like,  11-13 
Outline,  effect  of,  analogous  to  that 
of  pauses,  4,  5,  7 ; harmony  of, 
229-295  ; suggestively  indicating 
proportion,  50-59,  76-81 
Ovolo,  of  capital  in  Greek  architec- 
ture, 182,  185-189,  191,  198,  205. 
See  Like  with  Like,  Proportion, 
and  Ratios. 

Passtum,  temple  at,  187,  193,  221, 
255 

Painting, 5 ; brief  history  of, 300-308  ; 
Egyptian,  300  ; Greek,  300  : imi- 
tation of  nature  in,  243,  244,  296- 
298,  389,  390,  414  ; on  Greek 
exteriors  of  buildings,  189,  192, 
194,  416-418  ; decorative  or  ar- 
chitectural versus  pictorial,  296, 
298,  389,  390,  413-415.  See 
Colors. 

Pain  ting,  Sculpture,  and  Architecture 
as  Representative  Arts  ; 64,  102, 
128,  145,  146,  148,  158,  323,  361, 
415,  416,  423  ; analysis  of  the  es- 
say on,  428 
Pale  Colors,  304,  312. 

Pallas  of  Velletri  Statue,  97 
Pamphilus,  300 

Pantheon,  illustration  of,  223  ; pro- 
portions of,  224 

Parallelism — Art-Method,  3,  65,  78  ; 
in  color,  361,  363 

Parallel  Lines  in  Perspective,  hori- 
zontal, 233-238  ; vertical,  237 - 
240 

Parrhasius,  301 

Parthenon,  28,  29,  35,  97,  151,  186, 
190,  193,  194,  196,  197,  201,  202, 


INDEX. 


453 


Parth  en  on  — - Conti7i  ned. 

220,  222,  248,  25O-252,  256- 

258,  262,  263,  416,  418  ; illustra- 
tion of,  190  ; proportions  of,  21 1- 
218  ; stylobate  and  columns  of, 
as  photographed,  251 
Partial  effects  in  art  alike,  340-343  ; 
tones  in  music,  372—375,  398- 
404 

Pausanias,  26 
Pausias,  301 

Pediment,  Greek,  difficulty  of  cal- 
culating its  height  from  below, 
215-217  ; its  height,  same  appar- 
ently as  that  of  the  entablature 
added  to  a part  of  the  column’s 
capital,  198,  201,  202,  204-212, 
221  ; ratio  between  this  height 
and  the  height  and  breadth  of 
otherfeaturesof  the  Greek  temple, 
200-222  ; unsatisfactory  measure- 
ments of,  197 

Pennethorne,  John,  246,  249 
Penrose,  F.  C.,  29,  181,  183,  194, 
196,  197,  201,  202,  211,  220,  248, 
249,  250,  254,  255,  262,  263 
Pericles,  300 

Perspective,  aerial,  321-324 
Perspective,  linear,  effects  of,  as  dis- 
tinguished from  those  of  propor- 
tion. iii.  iv.  25-31.  35-38,  65,  178, 
179,  244,  246,  251-253  ; effects  of, 
considered  in  itself,  232-265  ; in 
architecture,  especially  Greek,  36, 
245-248,  255-258  ; in  causing  op- 
tical illusions,  240-246  ; in  differ- 
entiating actual  from  apparent 
measurements,  iii.,  24,  25,  32,  34  ; 
in  curving  and  leaning  forward  of 
Greek  entablature,  245-250,  2 5 5— 
258  ; in  horizontal  lines,  233-238  ; 
in  landscape,  237-239  ; in  vertical 
lines,  237-239 
Perugino,  302 
Pheidias,  97,  300 

Phigaleia,  temple  of,  1S6,  187,  190, 
194,  201,  208,  210,  218,  221,  219, 
220 

Phrase,  rhythm  of  musical,  18 
Phryne,  92 
Physical,  or 


Physiological  cause  of  gradation  in 
color,  410,  41 1 ; of  harmony  of 
color,  iv.,  v.,  vii.,  338,  347,  349- 
351.  353-358,  378-383,  39r-4°7; 
of  outline,  23-26,  229-243  ; of 
music,  iv.,  v.,  23-26,  338-348, 
356-358,  308-400,  403 
Physical  Characteristics  of  the  Ath- 
lete, Sargent,  88  ; Development 
of  Women,  Sargent,  88 
Physiology,  Text-Book  of,  Foster, 
267,  276,  345 
Pictures.  See  Painting. 

Picturesque,  The,  in  art,  425 
Pigments,  colors  produced  by  mix- 
ing, 311  ; producing  complemen- 
taries,  332,  333  ; study  of,  in  art 
and  science,  300-308 
Piloty,  K.,  364,  366 
Pinus,  301 

Pitch,  of  color,  5-7,  374  ; of  sound, 
5-7 

Plato,  26 

Pliny,  91,  92,  300,  301 
Plutarch,  300,  301 
Poetic  Principle,  The,  Poe,  431 
Poetry  as  a Representative  Art,  5, 
423  ; analysis  of  essay  on,  427 
Poetry,  measures  and  ratios  of,  16- 
18 

Polycleitus,  95,  97 
Polygnotus,  300 
Positive  Colors,  313 
Posture,  grace  of,  determined  by 
curved  lines,  290  ; Greek  study  of, 
141,  142 
Poussin,  305 
Praxiteles,  92,  97-100 
Prevost,  268,  274,  282 
Primary  Colors,  313,  326 
Principality — Art-Method,  3,  63, 
1 16  ; in  architecture,  284  ; in 
painting,  355,  356-358,  367,  368 
Principles  of  Athenian  Architecture, 
The,  181,  248,  254,  262.  See 
Penrose. 

j Progress — Art-Method,  3,  61,  67  ; in 
color,  412 

Proportion,  analogue  of  rhythm 
rather  than  harmony,  iv.,  v.,  vi., 
I 2,  3,  7,  10,  13-19,  23-26,  74, 


454 


INDEX. 


Proportion — Continued. 

115-117,  179,  430,  431  ; apparent 
not  actual  measurements  con- 
sidered in,  iii.,  iv.,  24,  25,  32,  34, 
38,  151,  179,  180;  architectural, 
34-42,  51-58,  116  144-228;  as 

developed  by  all  the  art-methods, 
61-67  note,  148  ; beauty  depen- 
dent on,  2 ; based  on  putting  like 
measurements  with  like,  v.,  8, 
10-19,  39-43,  52-56,  59,  60,  62- 
64,  68-84,  88,  1 16,  1 17,  120-143, 
184,  222  ; characterizing  natural 
forms,  13,  14,  73-78  ; complexity 
of,  15  ; confounded  with  linear 
perspective  and  so  misunderstood, 

iv. ,  v.,  25-31,  35-38,  178,  179, 
244,  246,  251-253  ; conscious, 
not  unconscious,  action  of  the 
mind  in  judging  of,  iv.,  v.,  23- 
27,  50,  178,  179,  430,  431  ; cor- 
respondences between  effects  of, 
and  of  harmony,  27,  31,  64-66, 
430,  431  ; curvilinear  indications 
of,  58—61 , 68-72,  88-135,  142, 
291  ; dependence  of,  on  fitness  or 
congruity,  iii.,  115,  116,  146-14S  ; 
distinguished  from  harmony,  iv., 

v. ,  25,  26,  430  ; effects  less  physi- 
cal than  psychological,  iv. , v. , 
24,  25,  50;  effects  of,  not  always 
distinguishable  from  those  of  con- 
tour, 148,  149,  173  ; facia],  85- 
87,  105,  106,  125-130 ; Greek 
architectural,  177-228  ; Greek 
conception  of,  v. , vi.,  26-30,  36- 
38  ; Greek,  of  human  face  and 
form,  120-130,  133,  134;  judged 
from  distance,  iii.,  35,  36,  180; 
judged  from  parts  not  wholes  of 
bodies  or  buildings,  v.,  152-154, 
222  ; importance  of,  2,  14,  15  ; in 
birds,  fishes,  quadrupeds,  trees, 
etc.,  77,  78  ; in  clothing,  79-82; 
indicated  by  imaginary  lines,  85- 
87  ; indicated  by  marks  of  like 
subdivision,  43-47,  152-161  ; in 
human  figures,  9,  58-60,  68-72, 
78-87,  115-143 ; in  or  between 
irregular  figures,  indicated  by  in- 
scribing them  in  square  or  curved 


regular  figures,  48-74  ; in  land- 
scapes, 13,  14,  73-77  ; in  stained 
glass,  78,  79  ; of  Parthenon,  211- 
218;  of  rooms,  150,  151  ; rec- 
tangular and  rectilinear,  44-58, 
68  ; that  objects  are  characterized 
by,  a statement  of  fact,  19  ; theo- 
ries concerning,  25-31.  See  Like 
with  Like,  Measurement,  and 
Ratios. 

Proportions  of  Typical  Man,  Sargent, 
D.  A.,  88 

Propylsea,  temple,  186,  190,  196, 
2x0,  218 

Protogenes,  301 

Psychical  or  mental  effects  in  con- 
nection with  harmony  of  color, 
344,  360,  375,  376,  406-408  ; with 
proportion,  iv.,  v.,  23-27,  50, 
343-345.  430,  431-  See  Har- 
mony and  Proportion. 

Pyreicus,  301 

Pythagoras,  vii.;  his  system  of  tone- 
harmony,  338 

Quality  of  sound  and  color,  5-7 

Radiation  in  color,  363,  408 

Raeburn,  305 

Raking  Cornice,  over  the  tympanum 
in  Greek  temple,  183,  185-189, 
191,  197,  198,  203,  206,  207,  213, 
214,  2x6 ; for  proportions  and 
measurements  of,  see  Like  with 
Like  and  Ratios. 

Randau,  Chateau  de,  51 

Raphael,  92,  180,  302 

Ratios,  9 ; as  used  by  Greeks  were 
simple  and  of  small  numbers,  19, 
39,  40  ; between  alternating  mem- 
bers the  numbers  need  not  be 
apparent,  1 1 7 , 127,  r65,  166;  be- 
tween architectural  members  in 
Greek  temples,  as  the  abacus, 
corona,  etc.,  and  the  capital,  cor- 
nice, and  stylobate,  188-191  ; be- 
tween these  three  and  the  archi- 
trave, the  frieze,  the  combined 
raking  cornice  and  cymatium,  the 
upper  diameter  of  columns,  and 
width  of  the  metopes  and  the 


INDEX. 


455 


Ratios — Continued. 

triglyphs,  191-195,  221  ; between 
these  six  and  the  entablature,  the 
tympanum,  and  the  upper  space 
between  columns,  195-199,  221  ; 
between  these  spaces  and  also  be- 
tween the  entablature  with  capi- 
tal and  the  pediment  and  the 
height  of  columns  with  or  without 
capitals,  198,  201,  202,  204-214, 
221  ; in  poetry  and  music,  16-18  ; 
not  apparent  to  consciousness 
when  causing  harmony  of  sound 
or  color,  iv.,  v.,  23-27,  343-345, 
353,  354,  404,  405  ! not  invariably 
apparent  when  causing  proportion 
or  rhythm,  19;  of  no  practical 
value  to  art  when  their  meaning 
not  understood,  29,  30  ; operative 
in  both  rhythm  and  proportion 
and  in  harmony  of  sound  and 
color,  iv.,  31,  64-66,  430,  431, 
recognized  in  the  degree  of  ful- 
filling art  principle  of  putting 
like  with  like,  v.,  8,  10-19,  39- 
43,  52-56,  59,  60,  116,  117,  120- 
143,  184,  222,  347-351,  354,  356, 
373-375,  377-383,  404,  405  1 simi- 
lar in  harmony  of  sound  and  of 
color,  338-347,  372-377,  394-404  1 
to  be  of  use,  they  must  be  of 
small  numbers,  v.,  ig,  39-42,  44, 

1 1 7,  143,  149.  See  Harmony, 
Like  with  Like,  and  Proportion. 

Realistic  art,  425 

Red  color  by  lamp-light,  315  ; in 
foliage,  317,  318 

Regensburg,  Bavaria,  256 

Regularity,  lack  of  in  Greek  measure- 
ments of  temples,  248,  250,  262, 
263 

Relief,  colors  in  backgrounds  of, 

387,  388 

Rembrandt,  304,  367,  412 

Renaissance,  painting  before  and 
after  the,  301  ; revival  in  archi- 
tecture, 226,  227 

Representation  of  nature  and  mind 
in  art,  420,  426-429.  See  Beauty 
and  Significance. 

Representative  Significance  of  Form, 


The,  423,  424  : analysis  of  essay 
on,  424,  425 

Repetition — Art-Method,  3,  61,  64, 
66  ; in  architecture,  148-15 r,  162- 
164,  168  ; in  color,  364-366,  368, 
410;  in  humun  figure,  1x6,  117  ; 
in  measurements  at  the  basis  of 
proportion,  162,  164,  175,  184; 
importance  of,  14  ; of  shape,  164, 
175  ; of  tone-harmony  and  that  of 
outline,  231,  232.  See  Harmony, 
Like  with  Like,  and  Proportion. 
Republic,  The,  of  Plato,  26 
Resonators  of  Helmholtz,  340 
Retina,  21,  22  ; illustrated,  350, 
380,  381  ; organs  of,  recognizing 
color,  viii.,  349,  350,  378-383  ; vi- 
bratory action  of  organs  of,  in  per- 
ceiving color,  349,  350,  353,  354, 
356,  360,  374,  377-383,  404,  405, 
411,412.  See  Vibrations. 
Reynolds,  Sir  J.,  122,  305,  367,  407 
Rhamnus,  temple  at,  153,  187,  219, 
221 

Rhodian  School  of  Sculpture,  98 
Rhyme,  230,  232 

Rhythm  and  Harmony  in  Poetry 
and  Music,  2,  13,  16,  23,  230,  232, 
233,  325,  328,  338,  342,  349,  373, 
397,  400,  403,  406,  41 1,  414,  423, 
424  ; analysis  of  essay  on,  430, 
431 

Rhythm,  analogue  of  proportion,  iv. , 
v.,  vi.,  2,  3,  7,  10,  13-19,  23- 
26,  74,  114-117,  179,  430,  431  ; 
connection  between,  and  harmony 
of  sound,  27,  31,  63-66,  343,  344, 
430,  431 
Rico,  308,  365 

Richelieu  Pavilion,  Paris,  150 
Rings  of  Ovola,  187 
Rods  and  Cones  of  the  Eye,  viii., 
349,  350,  380-383 
Romanesque  Architecture,  227 
Romantic  vs.  Classic  Art,  420 
Romney,  305 

Rood,  O.  N.,  ix.,  315,  321,  393,  396. 
4°9 

Room,  proportions  of  a,  150,  151 
Rosa,  S.,  303 
Roslyn  Chapel,  437 


456 


INDEX. 


Ross,  181 

Rotation  of  eyes  and  effect  on  per- 
spective, 237,  238 
Rousseau,  308 

Rubens,  304,  358,  359,  367,  376 
Ruskin,  59,  286,  368,  409 
Ruysbrack,  99 
Ruysdael,  305 

Samson,  G. , W. , 117 
Sandby,  305 
Sargent,  D.  A.,  88 
Scales,  color,  389-405  ; of  color 
and  music,  357,  358,  374,  375, 
389-405  ; Von  Bezold’s  color 
chart  of,  333-336,  390-393,  398, 
402,  404 
Schadow,  306 
Schaubert,  181,  248 
Science  of  Beauty  and  Laws  of  Geo- 
metric Proportion,  Hay,  46 
Scientific  study  of  color  necessary  to 
artists,  298-308 
Scopas,  98 

Scourging  of  Christ,  The,  Titian, 

324 

“Scribner’s  Magazine,”  88 
Sculpture,  excellence  of  Greek,  91  ; 
Greek  face  of,  conventional,  92- 
95,  126,  128  ; Greek,  modelled 
upon  nature,  89-101  ; posture  in 
Greek,  141,  142  ; proportions  in 
Greek,  83,  84,  89-101,  118-134, 
I4r,  142  ; styles  of  different  in 
Greek,  96-101 
Secondary  colors,  313,  326 
Segesta,  temple  at,  193,  221 
Selinus,  temple  at,  187,  igo,  193, 
195,  221 

Septimius  Severus,  Arch  of,  152, 
207 

Setting — Art-Method,  3,  65,  363 
Shade.  See  Colors  and  Light  and 
Shade. 

Shades,  312  ; and  tints  that  go  to- 
gether, 410.  See  Colors. 
Shadows.  See  Colors,  and  Light 
and  Shade. 

Shakespeare,  92,  180 
Shape,  and  measurement  connected 
in  effect,  148,  163,  164,  172,  173  ; 


beautiful,  when  its  outlines  are 
all  perceived  together  with  the 
least  conscious  visual  effort,  278- 
287,  293-295  ; horizontally,  278, 
279  ; vertically,  279-287,  See 
Contour,  Curves,  Ellipse,  Human 
Form,  and  Proportion. 

Sight,  Le  Conte,  ix.,  21,  238,  349, 
268,  272,  273 

Sight,  arts  of,  4-7  ; binocular,  266- 
295  ; field  of,  for  one  and  both 
eyes,  267-278 

Significance  in  beauty,  104-108, 
1 12,  139,  140;  of  human  face, 
104-106,  128  ; of  human  form, 
92-108,  112-114,  128,  129,  139, 
140  ; vs.  form  in  art,  104-108, 
112,  128,  129,  139,  140,  158,  423- 
432 

Significance,  The  Representative,  of 
Form,  analysis  of  essay  on,  424, 
425 

Simplicity  of  proportion  and  rhythm, 
14,  15,  20 

Sistine  Madonna,  437 

Socrates,  91 

Sonnavater  and  Knut  Entering 
Stockholm,  Hellquist,  363,  364, 
366,  369 

Sound,  arts  of  4,-7.  See  Harmony 
of  Sound. 

Space,  arts  of,  4 ; tendency  to  di- 
vide into  like  subdivisions,  10-13, 
28  ; correspondence  between  arts 
of,  and  of  time,  4-7,  10,  28 

Spanish  Lady,  by  Fortuny,  355 

Spanish-Roman  School  of  Painting, 

365 

Spectrum,  297,  298,  310,  31 1.  314, 
329-331 

Speech-harmony,  compared  to  ef- 
fects of  harmony  of  outline,  229- 
232,  431 

Speech-rhythm,  an  adaptation  from 
nature,  74,  go  ; compared  to  effect 
of  proportion,  74,  90,  112,  114- 
1 16 

Stained-glass  windows,  proportion 
of  human  figures  in,  78,  79 

Standards,  of  art-judgment,  and 
their  influence  on  production, 


INDEX. 


457 


Standards — Continued. 

433—437  ; of  measurement  in  hu- 
man form,  1 16,  118  : when  a 

complex  is  compared  with  a sim- 
ple figure,  rectangular,  and  curvi- 
linear, 48-72,  87,  1 34-143  ; or  is 
crossed  by  straight  lines,  57,  58, 
67,  68,  78-87,  125-129 
Steps  of  Greek  temple,  18S-190, 
194 

Stereoscopy,  principle  of,  270-276 
St.  Etienne  du  Mont,  Paris,  167-169 
Stimson,  J.  W.,  235 
St.  Mark’s,  Venice,  237 
St.  Paul’s,  Covent  Garden,  London, 
224,  225  ; illustration  of,  225 
Straight  lines,  increase  apparent 
length  in  their  own  direction, 
151,  152,  202  ; indicate  propor- 
tions when  at  equal  distances, 
drawn  really,  57,  58,  67,  68,  78- 
87,  125-129  ; or  imaginatively, 
85-87  ; or  suggestively,  56  ; paral- 
lel, vertical,  and  horizontal,  how 
brought  together  and  curved  by 
perspective,  233-265 
St.  Stephens,  Caen,  37,  154,  170 
St.  Sophia,  Constantinople,  illustra- 
tion of,  226 

St.  Sulpice,  154,  156,  157,  160 
Stuart,  18 1,  248 

Stylobate  of  Greek  temple,  183,  188- 
iqo,  194,  196,  201,  206,  208,  209, 
213,  214,  217,  250;  as  related  to 
other  members,  200-222.  See 
Like  with  Like  and  Ratios. 
Sublime,  The,  in  art,  425 
Subordination — Art-Method,  3,  63  ; 

in  color,  355,  358,  408 
Sunium,  temple  at,  187,  193,  219, 
221 

Sydney,  Australia,  university  at,  147 
Symington,  A.  J.,  298,  299 
Symphony,  Seventh,  437 
Symmetry — Art-Method,  3,  66  ; in 
outline,  249  ; in  color,  361,  411 
Syracuse,  temple  at,  193 
System  of  Geometric  Proportion,  A. 
Hay,  28 

Taste,  discrepancies  in,  112,  113  ; 


can  be  cultivated,  437  ; standards 
of,  not  inconsistent  with  original- 
ity and  genius,  433-437 
Temperaments,  human,  represented 
by  different  schemes  of  propor- 
tion, 1 16 

Temples,  Greek,  8,  12,  29,  30,  35, 
36,  44,  56, 116,  1 1 7,  248-264,  417, 
418 

Temples  of  zEgina  and  Basste, 
Cockerill,  ig,  29,  44,  178,  1S1, 
etc. 

Tenniers,  304 
Tennyson,  18,  433 
Texture,  color  of,  317 
Thebes,  temple  at,  246 
Themis,  temple  of,  at  Rhamnus,  187, 
193,  221 

Theory  of  Color,  Von  Bezold,  ix., 
333.  387 

Theory,  right,  necessary  to  right 
art-methods,  49,  140,  141,  253 
Theseum  or  Theseus,  temple  of,  36, 
156,  187,  189,  193,  196,  201,  210, 
211,  218-221,  224,  250,  252,  262 
Theseus,  statue  of,  97,  98 
Thiersch,  243 
Thompson,  219 
Timaeus,  Plato,  27 
Time,  arts  of,  4 ; correspondence 
between  arts  of,  and  of  space,  4- 
7,  10,  28 
Tintoretto,  303 

Titian,  92,  299,  302,  303,  324,  366, 
367,  407 

Tone,  the  term  as  used  both  for 
colors  and  sounds,  6 ; in  color, 
308,  312,  327,  355-358.  See 

Harmony. 

Tones,  partial,  in  music,  372-374, 
398-404 

Transition — Art-Method,  3 ; in  out- 
line, 61,  67,  148  ; in  color,  412 
True,  The,  in  art,  424 
Triglyphs,  12,  192 
Tryon,  308,  322 
Turner,  305 
Turpilius,  301 

Tympanum  of  Greek  temple,  183, 
195-198,  201,  204,  206,  207,  209, 
210,  213,  214  ; as  related  10  en- 


458 


INDEX. 


Tympanum — Continued. 

tablature  and  column-height,  201- 
222  ; same  height  as  entablature 
and  upper  space  between  columns, 
195-199,  221  ; unusual  height  in 
Parthenon,  215-217 

Unity — Art-Method,  3,  16  ; in  archi- 
tecture and  outline,  18,  19,  61, 
63,  1 16,  284;  in  color,  314,  325- 
328,  354,  355-358,  363,  368,  369, 
400 

Unconscious  action  of  mind  in  rec- 
ognizing effects  of  measurements 
causing  harmonic  ratios  in  sound 
and  color,  iv. , v.,  23-26,  64,  65, 
343-345,  404,  405 

Van  Dyck,  304 
Van  Dyke,  J.  C.,  365 
Van  der  Velde,  305 
Van  Eycks,  304 

Vanishing  point  in  perspective,  233 
Vase,  the  elliptical  outlines  of,  among 
all  people,  283,  284,  287,  288  ; 
illustrated,  283,  285 
Variety — Art-Method,  3,  18,  61,  62, 
64;  in  architecture,  164  ; in  color, 
328,  354-358,  364,  366,  369,  400, 
406,  430-432  ; in  human  form, 
1 16  ; not  inconsistent  with  effects 
of  tone  in  paintings,  355-358 
Velasquez,  303,  307 
Venetian  School  of  Painters,  302, 

304,  386 

Venus,  Anadyomene,  92  ; ascribed  to 
style  of  Praxiteles,  105  ; de’ 
Medici,  92,  97,  123 
Vernet,  PI.,  306  ; J.,  306 
Veronese,  Paul,  303,  360,  376 
Vertical  lines  as  affected  by  per- 
spective, 237-239  ; 257-262.  See 
Curves  and  Perspective. 
Vibrations,  in  organs  of  sight  or 
hearing,  as  distinguished  from 
waves  of  light  or  sound,  313, 
378,  note  ; as  influencing  concep- 
tions of  beauty  in  general,  112- 
1 14 ; common  multiple  for,  and 
ratios  of,  determining  harmony  in 
music,  28,  65,  66,  338-347,  372, 


375 , 398-401  ; determining  har- 
mony in  color,  347,  348,  373-375, 
377-383,  394-405  ; differences  be- 
tween those  producing  sound  and 
color,  372-377  ; numbers  of,  caus- 
ing each  of  the  colors,  402  ; physio- 
logical effects  of,  causing  harmony 
of  color  when  coalescing  in  retina, 
349,  350,  353,  354,  35&,  360,  377— 
383,  404,405,  410,4x1  ; similarity 
of  ratios  of,  in  harmony  of 
sound  and  of  color,  372—377,  394— 
405  ; similarity  of  those  producing 
harmony  of  sound  and  of  color  to 
the  beats  and  outlines  producing 
effects  of  rhythm  and  proportion, 
27,  31,  64-66,  343,  344,  430,431  I 
size,  rate,  and  form  of,  determining 
musical  harmony  and  quality,  338- 
347  ; unconsciousness  of  the  mind 
of  the  causes  of,  when  producing 
effects  of  harmony  of  sound  or 
color,  iv.,  v.,  23-26,  27,  64,  65, 
343-345,  404,  405 
Villegas,  308 
Vinci,  Leonardo  da,  302 
Violet  color  by  lamp-light,  315 
Vitruvian  Scroll,  12 
Vitruvius,  M.  P.,  26,  64,  117-120, 
122,  141,  150,  219,  222,  224,  246, 
251,  252,  256,  258,  261-264;  his 
trustworthiness,  120,  262,  263; 

The  Architecture  of,  198 
Von  Bezold,  ix.,  333,  387,  390,  392, 
401,  403,  404,  406 
Von  Klenze,  256 

Wagner,  21 1 
Walhalla,  The,  256 
Walker  Museum,  Chicago  Univer- 
sity, 54 

Warm  Colors,  303,  304,  313,  320- 
324,  384-388,  407,  408  ; in  aerial 
perspective,  321-324  ; in  back- 
grounds and  relief,  387,  388  ; in 
causing  harmony  by  preponder- 
ance, 327,  396,  note  ; in  comple- 
mentaries,  335,  336,  384-388,  407, 
408  ; indoors  and  out,  320,  321  ; 
in  shadows  and  not  at  different 
times  of  day,  3 19-321  ; quiet,  un- 


INDEX. 


459 


Warm  Colors — Continued. 

obtrusive  effects  of  color  obtained 
through  using,  385 

Waves,  producing  sound  and  color, 
distinguished  from  the  internal 
vibrations  experienced  in  the  ear 
and  eye,  313,  378,  note  ; occa- 
sioning color,  their  action,  349, 
350,  373-375.  377-383  i occasion- 
ing sound,  344,  349,  373,  374 ; 
size,  rate,  and  shape  of,  and  of 
vibrations  determining  musical 
harmony  and  quality,  338-347  ; 
their  shape  when  compound  illus- 
trated, 340.  See  Vibrations. 

Wedge,  shape  of  man’s  form,  13S- 
140 

Wheatstone,  274,  282 


White,  and  black  as  complemen- 
taries,  334,  335  ; light  containing 
all  the  colors,  309-3 11,  329-331 
Wiener  Bauzeitung,  24S 
Wilkie,  305 

Willesden  Church,  40,  154 
Window,  stained  glass  of,  indicating 
proportion,  78,  79 
Winckelmann,  306 
Wouvermanns,  305 

Yellow  color,  by  lamp-light,  315 
Young,  Sir  T.,  402,  403 

Zamagois,  308,  365 
Zeising,  A.,  27 
Zeuxis,  301 


OTHER* WORKS  BY  PROF.  GEO.  L.  RAYMOND 


The  Essentials  of  ^Esthetics.  8vo.  Illustrated  . . Net,  $2.50 

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work,  strong  and  thoughtful  in  its  conception.” — Worcester  Spy. 

“As  fine  lines  as  are  to  be  found  anywhere  in  English.  . . . Sublime  thought  fairly 

leaps  in  sublime  expression.  . . . As  remarkable  for  its  force  of  epigram  as  for  its 

loftiness  of  conception.” — Clevela7id  World. 

“ There  are  countless  quotable  passages  in  Professor  Raymond’s  fine  verse.  . . . 

The  work  is  one  of  unusual  power  and  brilliancy,  and  the  thinker  or  the  student  of  liter- 
ature will  find  the  book  deserving  of  careful  study.” — Toledo  Blade. 

“ . . . ‘Columbus’  one  finds  a work  which  it  is  difficult  to  avoid  injuring  with  ful- 

some praise.  The  character  of  the  great  discoverer  is  portrayed  grandly  and  greatly. 

. . . It  is  difficult  to  conceive  how  anyone  who  cares  for  that  which  is  best  in  litera- 
ture . . . could  fail  to  be  strengthened  and  uplifted.” — N.  Y.  Press. 

Dante  and  Collected  Verse.  Just  issued.  160,  cloth  extra,  gilt  top.  $1.25 
G.  P.  PUTNAM’S  SONS,  New  York  and  London. 


CL- 


, This  Book  is  Due 

^pr  19 '32  Q 

$M9*36  p 

DEC  6 79 


70127R269C  v.7  36493 


